Bored Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⠿⠿⠿⠿⢿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⢀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠋⠉⠙⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⢀⣤⣶⣾⠿⠿⠟⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⣹⣿⣇⠙⢿⣦⣀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⣠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠹⣿⡄⠀⠙⠻⣷⣦⡀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⠀⠀⠙⣿⣦⠀⠀⠈⠻⣿⣆⠀⢠⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⣾⣿⣤⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠸⣿⡄⢸⣿⠁
⠀⠀⠀⠀⠀⢸⣿⣼⣿⡿⠋⠁⠀⢀⣀⣨⣭⣭⣽⣏⣉⣉⠉⠁⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠈⠙⠿⣷⣄⣿⣧⣾⡟
⠀⠀⠀⠀⠀⠈⣿⣿⣿⠃⣠⣴⣾⠿⠛⠋⠉⠉⠉⠉⠛⠻⢿⣶⡄⠀⠀⠐⠿⠟⠋⠉⠉⠉⠉⠛⠻⢿⣶⣤⡈⢿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠀⣿⣿⠃
⠀⠀⠀⠀⠀⣀⣤⣿⣿⠀⠀⣀⣤⣴⣶⣾⣿⡿⣶⣦⣄⠀⠀⠀⢹⣿⡀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⣿⣏⣤⣴⣦⣄
⠀⠀⠀⠀⣾⡟⠛⢻⣿⠀⠸⣿⣏⠉⠙⠿⠟⠀⢀⣽⡿⠃⠀⠀⠀⣿⡇⠀⠀⢺⣿⣏⠁⠘⠿⠿⠋⠙⢻⣿⠆⠀⣿⡿⠛⠉⠉⣿⡇
⠀⠀⠀⠀⣿⣆⠀⢸⣿⠀⠀⠘⢿⣷⣄⣀⣤⣶⡿⠛⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠙⢿⣷⣤⣀⣀⣀⣴⣿⠏⠀⠀⣿⡇⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠙⢿⣦⣼⣿⠀⠀⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠈⠙⠛⠿⠛⠋⠁⠀⠀⢠⣿⡇⢀⣤⣿⠟
⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣶⣤⣄⣀⣀⡀⠀⣀⣀⣀⣤⣤⣶⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠟⠿⠿⠿⠿⠟⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⣿⣄⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣧⣾⡿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⣴⡿⠃⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⢿⣷⣄⠀⠀⠀⠀⠙⣿⣦⠀⢀⣾⡿⠁⠀⠀⠀⠘⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⠿⠛⠉⠀⠀⠈⢻⣷⡄⠀⠀⠀⠘⣿⣦⣿⠟⠀⠀⠀⠀⣠⣾⠟⠛⠻⠿⣷⣶⣤⣄⣀⡀
⠀⠀⠀⠀⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣶⣤⡀
⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠘⣿⡆⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡀
⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⣿⡇⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣇⢀⠾⠽⣝⡀⠀⣀⡀⠀⡇⠀⠀⠀⢀⡠⢒⡪⣉⠭⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⡏⠀⠈⠉⠹⠋⠋⡇⠀⢨⠂⠀⢠⠎⡫⣡⣤⣐⠶⢢⣾⣵⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡁⠠⠁⡄⠈⠀⠁⣃⡠⠎⠉⠐⢼⢈⢸⠩⠜⡝⢃⠀⢠⠘⢢⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⠒⠺⠙⡀⠀⠓⠀⠀⢠⠋⠀⠀⠀⠀⠈⡾⡘⡄⠀⠑⡄⠀⢀⠤⠄⠾⢠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠇⠱⣀⠙⠁⡠⠃⠀⠀⠀⠀⠀⠀⠁⢹⢈⠆⠀⠸⠀⠀⠀⣠⠃⡇⠀⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡇⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠃⠀⣰⠇⠀⠀⠀⡏⠀⢡⡀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠁⠀⠰⢣⠑⢄⢀⡰⠁⠀⠀⠱⡀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠉⠐⡖⠒⠒⠂⠒⠃⠀⠀⠀⢸⠀⢠⢇⣸⠤⠤⣀⡀⠀⠀⠀⠀⠑⣄⠀⠀⠙⡄
⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⢆⠀⠀⠀⣀⡱⠖⠰⢄⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣿⡒⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⢱⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⠤⠴⠓⠈⠁⠈⠉⠋⠒⠈⠉⠁⠀⠒⠒⠒⠒⠒⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠊⠑⠊⠉⠉⠓⠐⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠶⠄⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⣈⣤⠶⠛⠀⠈⠁⠀⠀⠀⠀⠀⠁⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⢀⣉⠤⠶⣾⡇⠀⠀⠀⠀⢀⠀⠙⠂⢄⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣰⠋⠀⠀⠀⠀⢹⡠⢶⠂⡀⠸⠀⠀⠀⠀⠑⣄⠀⠀⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⡰⢋⡤⢤⡀⠀⡇⠀⠀⠀⠀⡴⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⢠⠁⢈⠀⠀⠘⡆⠳⣀⠀⠀⣸⠁⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⢀⠂⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⣜⠀⠀⠑⠠⠀⠀⠀⠈⠉⠁⠸⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡼
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡀⠄⠤⠐⠠⠤⠁⠒⠁
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡤⢲⠄⡦⠐⠒⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⢤⡀⠀⣠⠤⠴⠥⠆⠁⠈⣰⠋⢯⡲⠆⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠲⠤⢀⣀⠀⠀⠀⠀⢘⡆⢖⢒⡒⠺⠿⠳⠤⠀⠠⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠁⠈⠉⠉⠈⡇⠸⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⡐⠁⢹⠇⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇⢘⠛⢢⡄⠀⢸
⠒⠶⠤⠤⠤⠼⣅⣀⡉⠒⠠⢀⡀⠔⠂⠈⠀⢱⡄⡇⠈⢠⠎⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠢⠤⠔⠲⣕⣸⡼⠟⢧⠴⠛⠒⠒⠒⠚⠳⠤⠤⠤⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠉⠁⠐⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠳⠤⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠱⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⣀⣠⠤⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠞⠈⠛⠉⢅⣈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠐⠒⠒⡖⠋⠉⢁⠞⡔⠉⠑⠢⣄⠀⢀⠔⠋⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⡇⠀⠀⠀⠈⢳⡏⠀⠀⠀⠀⡇
⢀⡤⠤⠀⠀⠒⠒⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⡄⠀⠀⠀⢳⠀⠀⠀⢀⣼⣷⣤⣤⣀⣀⠷⡄
⠇⠁⣖⠆⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠈⢧⡀⣠⠎⠈⢸⣄⣀⡤⠋⠀⠙⣆
⢰⡀⠀⣀⠀⠀⠸⡇⢠⡄⠀⠀⠀⠀⣠⠔⠒⠶⢤⣤⠇⠀⠀⠀⠀⠀⠙⠧⣤⣤⢾⠁⠀⠀⠀⠠⢄⡈⣇
⢸⣃⠈⠛⠀⠀⠀⠈⠛⣅⣷⠀⠀⠀⣇⠐⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⢄⣀⡠⠃⣸
⠈⠲⠦⠤⠴⠒⠒⠊⢻⡏⠈⢓⡶⠖⠋⠓⠒⠒⠋⠑⠦⣄⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁
⠀⠀⠀⢀⢸⠀⠀⠀⢨⣠⠖⠋⠀⢀⡀⠀⠀⠀⢀⡄⠀⠀⠈⢙⠖⡶⠶⠤⢤⣤⠤⠴⠖⠒⠋⠙⠒⠒⠒⠂⠀⠤⠤⠤⠀⣀⣀⡀
⠀⠀⠀⠸⠘⡀⠀⢠⡞⠁⠀⠀⠀⢸⠁⠀⠀⠀⢸⠀⠀⢀⠔⢁⣰⠧⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈
⠀⠀⠀⢀⡆⠧⢤⡏⠈⠓⠤⣀⠀⠙⢲⣶⣤⡤⣼⡤⠴⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢊⠠⠆⠁
⠀⠀⠀⠘⢅⡀⠀⠙⢦⡀⠀⠈⠙⠒⡟⠀⣹⣀⣏⡀⠒⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢊⠀⠂⢈⠀⡇
⠀⠀⠀⠀⢀⠋⠉⠒⢦⢬⣑⢲⣆⡒⠇⠀⡇⠈⠢⣼⢹⠒⠒⠤⢄⡉⠐⠂⠀⠤⢀⡀⠀⠀⠀⠀⠀⡠⠔⢈⠄⠊⠀⠠⠀⠀⡇⠁
⠀⠀⢠⣃⠌⠀⠀⠀⢰⢼⠀⠈⢳⣒⣀⡴⠃⠀⠀⠸⢸⠤⣀⡀⠀⠀⠉⠁⠒⠠⠄⣈⡉⠁⠒⡖⣉⠄⠊⠀⡠⠐⠁⠀⠀⠀⡧⠶
⠀⠀⠒⠊⠀⠀⠀⠀⠈⠉⠀⢀⣎⡇⡇⠀⠀⠀⣠⡟⢸⠀⢀⡼⠁⠒⠦⢄⡀⠀⠀⠀⠀⢹⢘⠋⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⡇⡟⠿⠛⡿⢯⠟⢸⠛⣯⠀⠀⠀⠀⠀⠀⠉⠐⠂⠄⡜⢸⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡿⠢⠶⠀⡴⣷⢺⡶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠁⠰⠿⠶⠒⠒⠒⠒⠒⠒⠒⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢶⠆⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠋⠉
⠀⠀⠀⠀⢀⣴⠟⠁⠸⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣐⠲⠦⠄
⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠴⠀⠉
⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠒⠉⢉⡐⠠⢄⣀⠀⢼⡆
⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⣈⠑⠂⠬⠙⠲⢽⣄
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⢰⡆⢀⡀⠀⠀⠰⠓⠈⠙⠲⢤⡄⠀⠈⠓⢤⡀
⣼⠀⠀⠀⠀⠀⠀⠀⣠⣔⠋⠁⠀⠀⠀⢸⠇⣸⠹⠟⠂⢄⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠙⢄
⣙⠶⣀⠀⠀⠀⠀⠀⠀⠈⢙⣢⡄⠀⠀⠞⢀⡇⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⡇⢀⡴⠶⢦⡈⢧
⣧⠔⡿⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠘⠳⡀⠀⠀⠀⠀⣷⡀⠀⣀⡴⠁⡞⠀⠀⢀⡇⠈⡇
⠈⠐⠧⠤⠤⠠⢄⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠐⠠⡀⢀⣠⡟⠀⠀⠀⠀⠄⠀⠰⠒⠉
⠀⠀⠀⠀⠀⠀⢀⣁⡄⠀⢀⠼⠆⠀⠖⠢⡀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⣰⠋⠀⢀⣠⣀⡇⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠹⡄⠈⠑⠒⠃⠻⣤⣀⣀⡀⠀⠙⠢⡀⠀⠀⠠⠴⠂⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠂⠉⡷⠦⡭⠻⢤⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠖⠋⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢰⠃⢀⠎⠉⠉⠉⠉⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠁⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡰⠃⠀⣸⠁⠀⣀⡤⠒⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⣸⣄⢀⡀⢧
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣸⣱⠁⠀⣰⣃⡴⢚⡡⠀⣀⠀⠀⠉⠢⠤⣤⠔⠒⠉⠉⠀⠈⠓⢌⡙⣆⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⠴⠋⠀⠉⠧⢤⣞⣁⣀⡦⣄⣤⠴⠚⠒⠂⠒⠛⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠉⠉⠐⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡦⣄⢀⣀⡬⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠦⢄⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠟⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠳⣄⡤⠴⠒⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⣶⢋⣉⣀⡀⠀⠐⠲⠎⣳⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠁⠀⠀⠰⢡⡏⠀⠀⠙⠲⡄⢀⡞⠁⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠘⣾⠀⠀⠀⠀⢸⡇
⣠⡤⠐⠒⠒⠒⠒⠒⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢳⡀⠀⠀⠀⢻⡀⠀⠀⠀⣰⣿⣶⡦⢤⣄⣸⠷⡄
⡇⠁⢞⡂⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢧⡀⣠⠞⠁⠀⣧⣀⣠⠴⠋⠀⠘⣆
⢫⠀⠀⣀⠀⠀⠀⣿⠀⣠⠀⠀⠀⠀⠀⢀⠤⠶⠦⠤⣄⡼⠁⠀⠀⠀⠀⠀⠙⠧⣄⣀⣼⡏⠀⠀⠀⠀⠤⢄⠘⣇
⢸⣇⠀⠷⠁⠀⠀⠈⠑⢻⡠⡇⠀⠀⠀⡇⠠⠚⠻⠗⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢀⡀⠀⣠⠇⢸
⠘⣼⣄⣀⣤⡤⠤⠤⠲⡶⡛⠹⠤⣤⡤⠞⠲⠤⠤⠴⠚⢦⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⡴⠎
⠀⠀⠀⢸⠘⡀⠀⠀⠀⡇⣇⡤⠖⠁⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠒⠦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⠤⠶⠾⠭⠤⠄⣀⣀⣀⡀
⠀⠀⠀⠀⡄⡇⠀⠀⢀⡷⠋⠀⠀⠀⢐⠇⠀⠀⠀⠀⡏⠀⠀⠀⣠⠞⢡⡇⣀⠤⠜⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠒⠲
⠀⠀⠀⠀⡇⢱⠀⢠⠟⢦⣀⠀⠀⠀⢼⣀⣀⠀⠀⠀⡇⠀⢀⣞⠥⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⡡⠐
⠀⠀⠀⠀⡷⡙⠛⢻⡀⠀⠈⠑⠢⣄⣀⣸⠛⢿⡟⢻⢟⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⡁⢴⢹
⠀⠀⠀⠀⠑⢢⢄⣂⠉⠳⢤⣀⠀⣀⡈⡿⠀⢸⠶⡼⠦⣄⣈⠉⠐⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⡡⠔⠁⠀⢼⠀⡄
⠀⠀⠀⠠⢁⠎⠀⠀⠉⡖⢶⠬⣽⠧⠈⠃⠀⡏⠀⠈⠳⡇⡿⠈⠁⠒⠤⠤⣀⡈⠁⠒⠠⠤⣄⣀⠀⠀⠀⣀⠴⢊⡡⠔⠁⢀⠤⠊⠀⠸⠀⡇
⠀⠀⢠⢧⡌⠀⠀⠀⠀⡷⡏⠀⠀⢹⣍⣤⠴⠃⠀⠀⠀⡇⡷⠦⢤⣀⠀⠀⠀⠈⠉⠒⠒⠤⢄⡀⠉⢱⢊⡠⠖⠉⢀⡤⠂⠁⠀⠀⠀⠀⡖⡇
⠀⠀⠈⠒⠀⠀⠀⠀⠀⠉⠁⠀⢠⢯⡇⢀⠀⠀⠀⢀⣞⡃⡇⠀⣀⠞⠉⠐⠒⠤⢀⡀⠀⠀⠀⠀⡏⢹⠁⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣳⡇⢨⠿⣛⣿⠿⡽⠇⡟⠻⡅⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢤⡇⢰⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣻⠲⢴⠇⢠⣾⡦⣧⣲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣅⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠒⠉⠉⠉⠉⠙⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠔⢐⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⣀⣀⣀⡠⢤⣄⣀⡑⠀⣤⠀⠀⠀⠀⠀⠈⢤⡽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠄⠀⠀⢀⡤⠒⠒⠲⠀⠉⢩⡋⠀⠀⠀⠀⣈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣡⠶⠬⡶⡆⠀⡰⠋⠉⠓⢄⡼⠀⠀⠀⢧⡤⠞⠡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀⠑⣠⣔⠚⠁⠀⢇⠠⠤⠴⠊⡤⡖⠏⣄⣀⣊⣳⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⠙⢢⡑⠀⠁⠀⠀⠀⠀⠠⢀⡎⠃⣀⣀⡅⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣋⠈⢯⠏⡐⠒⣒⢉⠉⢀⠀⠘⠣⣀⠖⠀⠀⣡
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠠⠤⠄⢴⠉⠉⠉⠒⢷⡀⠀⢤⠖⠚⠦⠤⠚⠓⠤⠖⢺⣃
⠀⠀⠀⠀⠀⠀⠀⢇⠀⢈⠉⠉⠉⠐⢺⣄⠀⠀⠀⣤⡭⢏⡇⠀⠀⠀⠀⠀⣤⣤⠴⠟⠁⠀⢀⡉⠭⠝⠒
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢲⡉⠉⠻⣉⣽⣿⠇⢘⠦⢄⣀⣀⣀⣤⣿⠏⠉⠉⢹⠉
⣠⣤⣤⡤⠀⠀⠂⠚⠒⠒⠒⠠⠤⠤⠙⣓⣒⠛⠛⠁⠀⢺⡀⠀⠙⣄⣴⣿⠟⠐⠐⠀⢸
⠘⡄⠀⠀⢈⠉⠁⠒⠂⠤⠤⣀⣀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠛⠛⠛⠻⠋⠥⠤⠀⣀⢀⣸
⠀⢸⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠲⠒⠤⠤⠤⢄⣀⣀⠀⠀⢀⣀⠤⠔⠊⠁
⠀⠘⠒⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⡈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠀⠤⠄⣀⣈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⠤⠤⢀⣀⡀⠀⢸⠀⢀⡀⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣔⢀⣰⣃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠑⢄⠀⠀⠀⠄⠀⠑⠀⢆⠀⡤⠀⠀⠀⠀⠉⠀⠴⠀⠀⢩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠦⠐⠁⡀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠰⠎⠈⠘⠁⠋⠀⠀⠀⠀⢀⡄⠀⢠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠁⣦⠀⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠠⠃⠀⢀⠔⠀⠀⠀⠀⠀⠈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⣶⢤⢌⡀⠄⠀⠀⠀⠒⠦⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠠⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠒⢷⣺⡀⢁⡪⠃⠻⡾⠆⠐⠀⠔⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠱⡒⠠⠐⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠸⠁⠄⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⢀⠀⠀⢱⣄⠀⠀⠀⠉⠂⠀⢀⠀⠀⠀⠀⠀⠀⠊⠈⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠣⠤⠊⠉⠚⢦⣻⡀⠀⠀⠀⢀⠜⠁⠀⠀⠐⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⠀⠁⠉⠀⠈⠈⠁⠀⠀⡠⠃⠀⠀⠀⢀⠀⢹⠉⢃⠀⠀⠀⠀⠀⠀⠄⠘⠳⠞⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡖⢀⡀⠀⠐⠒⢒⣒⣰⠊⠀⠀⠀⠀⠀⠂⠀⠀⢦⠤⠀⠀⠀⠀⢀⠀⠀⢀⣀⡃⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠂⢀⡀⠀⠀⠤⠄⠒⠉⠀⠈⠂⠀⠀⡠⢣⠀⠀⠀⠸⠀⢣⠀⠀⠀⠀⠆⠠⠤⠤⠄⠀⠀⡠⠀⢀
⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⠀⠀⠂⠀⠀⢰⡅⠀⠂⢠⠁⢸⢁⣀⡀⢀⠄⢀⠄
⠀⠀⠀⠀⡠⠀⡌⠀⠄⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⢀⣀⣈⣄⣈⡁⠀⠀⠀⠀⠀⠂⠀⠤⠀⠀⠀⠀⢀⡀⣈⠈⠀⠐⠂
⢀⡀⠁⠐⠁⠀⠀⠀⠀⢀⠦⠀⠀⠀⠀⠐⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠃⠀⠀⠘⠀⠰⠁⠤⠤⠤⠤⠤⡀
⠀⠁⠀⠀⠀⠀⠈⠀⢀⠺⣤⠤⣤⣀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⢀⡀⢀⣀⣀
⠂⠆⠀⠑⠤⠀⢄⠠⠎⡜⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈
⠀⠔⠂⡀⠀⡀⢀⠤⠔⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠁⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠤⣴⠀⠑⣠⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⣄⣠⣠⡄⣮⣀⣀⠀⣤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠛⠙⢅⡐⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢙⢉⣭⣺⠷⠖⢲⠿⣾⠦⠶⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢨⠟⣿⢉⣑⣢⢟⢈⣟⣅⣠⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠠⣧⢤⣛⡿⡤⣿⠟⠻⡻⠿⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⢹⡿⢾⣰⡮⢽⣄⣠⣓⣺⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢑⣴⡽⣖⣾⠋⠉⠻⡿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢠⣉⣻⠟⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣄⣀⠀⠀⠀⠀⢀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠻⡁⠣⠐⠈⠑⢄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⢘⡄⠀⠀⠀⠈⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣴⢫⣵⠀⠀⠀⠀⠐⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡈⠈⠈⢀⡆⠀⠀⠀⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠈⢉⡠⠀⠀⠀⢹⡄⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⢀⠈⢦⠀⠀⠀⢀⣉⣀⠀⠈⡄⠀⠀⠀⠈⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠂⠀⠀⡱⣄⡀⠀⠀⠀⢉⡠⣷⠀⠀⠀⠀⠘⡈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⠌⠑⠒⠒⢉⡜⠈⡆⠀⠀⠀⠀⢀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠈⠚⠒⠐⣒⣉⡀⠀⢡⠀⠀⠀⠀⠈⠑⠺⠷⢶⣄⣀⣀⣀
⠀⠀⠐⠒⠀⠀⠀⢂⠀⠀⠀⠀⡐⢀⣆⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠒⠒⠚⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣂⣄⣀⣀⣂⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠉⠀⠀⠚⠒⠚⠛⠛⠉⠉⠛⠛⠓⢒⣦⡄
⠀⠀⠀⠀⠀⠀⢀⣤⠞⣏⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣖⣚⣉⠉
⠀⠀⠀⠀⠀⣴⠟⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠛⠛⠃
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣖⡚⠉⠉⠒⣤⡀
⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡿⠖⠀⢘⠲⢬⣝⡲⠤⣝⣅
⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⢉⡁⠀⠀⠀⢀⣿⠖⠦⢍⣀⠀⠙⠳⣄
⠀⣸⠁⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⠀⣼⠁⡟⣶⠦⣼⠀⠀⠀⠀⠈⢧⠀⠀⠀⠑⢄
⠀⢛⡦⢀⠀⠀⠀⠀⠀⠈⠑⢢⡀⠀⠀⠏⢰⠃⠀⠀⠈⠳⡀⠀⠀⠀⢸⠀⢠⠤⠤⡈⢣
⠀⣯⠔⡏⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠚⢆⠀⠀⠀⠀⢳⣀⣀⣀⠜⢠⠃⠀⠀⡿⠀⣇
⠀⠈⠘⠧⠤⠔⠢⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠓⢤⣀⣠⡿⠀⠀⠀⢠⡀⠀⠓⠊⠀⠀⢹
⠀⠀⠀⠀⠀⠀⢀⣨⠧⠤⠤⡞⢻⠁⡟⠢⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⡏⠀⣠⠴⣶⢧⠈⠀⠀⠀⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠳⢤⣀⣉⣁⣘⠶⣖⠤⢤⡄⢈⡷⠀⠀⠒⠉⠁⠀⠀⠀⠀⢀⣠⠴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢉⠏⢉⠿⠤⠤⠤⠤⠤⠤⠤⠄⠒⠊⠉⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢀⠎⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⠎⠀⡸⠁⠀⢀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣫⠏⠀⣰⢃⡠⢚⠉⠀⠀⠈⠑⠤⣀⣠⠤⠔⠒⠉⠉⠻⣕⠺⡄
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠯⣀⠴⠋⠉⠳⠥⣠⠋⢀⣦⣀⣀⠤⠓⠒⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠴⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⡙⢆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠱⡈⢷⣅⠙⠀⠀⠀⠀⠀⠀⡜⠁⠀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⢤⡀⠀⢁⣀⠦⣀⡔⠀⣠⠚⡄⢡⠃⠀⠀⠀⠀⢀⠞⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡒⢦⢄⡱⠚⠁⠀⢀⣿⡤⠊⣁⠠⠕⠃⠀⡀⠀⠀⢠⠎⠀⡠⠃
⠀⠀⠀⠀⠀⣀⠠⢄⠀⠀⠀⠀⢀⡀⢀⡤⠊⠁⠉⠉⠉⠐⠒⠙⢋⠙⣷⣆⣠⠴⠋⠀⢀⡼⠿⠁⠐⠦⣁⠀⠀⢠⠏⠀⡜⠁
⣜⣿⣿⣿⣿⡿⢲⡌⠉⠉⠀⠀⠈⡄⠀⣇⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠐⠀⠀⠀⠀⠀⣠⠜⠛⠉⠁⠒⢄⠀⢀⠇⢀⠎
⠉⠈⣍⠧⠦⠙⠉⠑⠠⢄⠀⠀⢀⠃⠀⠈⣲⠖⠓⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢱⡆⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⢌⡲⠎⣀⣠⠎⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⣀⠤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡠⠗⠂⠉⠀⠀⠀⠀⠤⠤⠠⠵⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠲⡀⠀⠀⠀⠘⠢⠤⠤⠐⠒⠈⡇
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣀⡰⣖⡄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⢄⡀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⡤⠒⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⡠⠙⠄⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠘⡍⠥⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡵⠁⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠰⠁⠰⠚⣠⠀⣀⡣
⠀⠀⠀⠀⠀⠀⡈⣤⠀⢿⠐⠠⠤⠤⠤⠤⠞⡻⢿⡟⠉⢹⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⢀⣠⠁⠀⠀⠀⠀⠁⠊
⠀⠀⠀⠀⠀⠘⠤⠠⠖⠉⠣⣤⢤⡤⠔⠂⠙⠀⠀⠉⠲⢤⡀⠀⠜⢀⣀⠠⠤⠔⠒⠉⠇⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠜⠊⠀⠀⠀⠀⠀⠀⠀⢩⢙⠉⠁⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⢿⣿⡿⠋⠻⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡀⠈⠁⠠⢤⡀⠈⠙⠿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠛⢿⣇⠀⠈⠿⠖⠀⡴⣒⠂⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠸⣿⡀⠀⢀⠀⠘⠁⢉⣼⠥⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢻⣷⣄⣈⣉⣠⣴⠋⠀⣤⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡇⠀⠀⠀⠙⠿⠿⠿⢋⣘⣄⡀⠈⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡏⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⢻⣿⠀⠀⠀⠀⢠⠎⠿⠿⠿⢻⡆⠀⠀⠘⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠿⠖⠒⠒⠚⠉⠀⠀⠀⠀⣼⣿⡄⠀⠀⠘⣄⣤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⠻⢿⣷⡀⠀⠀⡏⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣦⡤⠞⠉⠓⠋⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⢶⣤⣤⣤⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣠⣾⣿⠟⣻⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣰⣿⣿⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠙⣿⣿⣿⣿⡟
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢤⡤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣤⠄⢸⣿⣿⣿
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⡿⠀⠈⠾⢻⡇
⠀⠀⠀⠀⢀⡿⢋⣁⣉⠙⠿⠏⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠉⠀⠀⠀⣦⡾⠃
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠙⣷⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⡀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠇⠀⠀⢠⣿⣿⣿⣿⣿⣷⡄
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄
⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠉⠻⢿⣿⣿⣿⣿⡿⠟
⠈⠛⠿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠉⣻⡶⢦⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⡴⠞⠛⢷⡄⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣤⡀⠀⠉⠛⠿⠿⢿⣿⣿⣿⡿⢶⡶⢶⣤⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠈⠙⢷⣶⠃⠀⠀⣰⣯⠀⠈⣿⠀⣿⡀⣿⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠙⠛⠿⢿⣍⡙⠷⠶⠿⠶⠛⠛⠁⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⢀⣀⣈⣛⣷⣦⣤⣀⣀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠙⠻⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡟⣿⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠛⠛⢻⡇⣿⠟⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⡇⢹⡂⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣾⡉⣯⣹⠛⠛⠛⢿⡅⢸⠟⠛⠛⢻⣉⡏⣹⡷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣥⣤⣼⣭⣥⣤⣤⣤⣤⣼⡇⣿⣤⣤⣤⣤⣤⣬⣭⣤⣤⣽⣷
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣇⣻⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣟⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠹⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠉⠉⠉⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣼⠷⢤⣤⣄⣠⣤⣤⠤⠤⠤⢌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣼⠃⠀⣠⡤⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡏⠀⠘⠁⠀⠀⡀⠀⠀⠀⠀⠀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⣠⠶⣿⣿⠀⠐⣎⠙⣿⡿⠁⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠈⠙⠲⠞⠁⢤⣤⠌⠉⠉⣠⢤⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⢆⠌⠝⠄⠀⠀⣀⣤⣤⠀⠐⡍⠱⠑⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⣀⠇⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠈⠑⣄⣀⣀⣀⣜⠁⠀⢤⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠗⡮⠤⡴⠋⠉⠉⠉⠈⠻⠒⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣥⣴⣃⡠⠄⠀⠀⠠⣤⣙⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⣿⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⠙⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠹⣦⣀⣀⡀⠀⠀⠀⠀⣀⣸⡗⠀⠀⠀⠙⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠐⢀⣤⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣦⡀⠘⢂⢿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠛⠛⠿⠿⣿⣿⣾⡆⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠓⠂⠀⠠⠤⢤⣌⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢧⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡋⠀⠈⠙⠓⠲⢦⠞⠭⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡂⢀⡛⠀⠀⠀⠀⠀⢸⣤⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠌⠋⠉⠀⢰⣶⠞⢐⡟⠛⠋⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠇⠀⠀⢀⠀⠈⡟⣠⢚⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠰⣆⢀⠄⠊⠣⠀⠉⠁⡄⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠒⠒⠓⠋⠄⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢀⠄⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠐⢦⣰⡁⠀⠀⠀⢠⠊⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠙⠉⠓⢶⣶⠮⠴⠦⢤⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡴⠛⠃⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣄⠀⠀⠈⣳⠇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣬⣿⣶⣿⡟⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡾⠿⠟⠁⢠⣿⣦⣤⣀⣀⣀⣤⣶⣤⡤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡏⡄⠀⢀⡠⠿⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠾⠗⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⢀⠠⠐⠀⢹⠟⠭⠹⠋⠈⠁⠂⠄⠀⠀⠀⠀⢫⢉⠄⣿⡇
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠂⢴⡥⠀⠀⠀⠀⠰⠀⠀⠀⠀⠛⠚⠋⠕⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠁⠄⠀⡀⠀⠀⠀⠀⠐⢱⠤⠁⠢⡀⠀⣠⣾⣿⣿⣦
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠂⢀⠠⠀⠀⠈⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⢘⠏⠒⢸⠿
⠀⠀⠀⠀⠀⠈⢀⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⢘⠀⠀⠠⠈⠀⡠⢞⡇⠐⠒⠢⡀
⠀⠀⠀⠀⠀⢁⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠⠀⡡⠀⠈⠀⠀⢇⠀⢀⠀⠘⠀⠀⠂⠀⠸
⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠀⢀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠄⠀⢄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣎⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⣀⠄⠐⠀⠀⠀⠀⠁⠀⠘
⠀⠀⠀⠀⠀⠐⠉⠙⠩⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠃⠁
⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⣀⠤
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⠶⠶⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⠇⣷⢰⡗⢰⡇⢿⣤⣤⣤⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣠⡶⠿⠶⢾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠟⠈⠃⠘⠃⠀⠀⠀⢸⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⢻⡟⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠻⣶⡘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠶⠶⠶⠶⠶⠀⠀⠘⢷⣤⡾⠁⠙⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠃⠀⠀⠀⠀⢸⡇⠀⢀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣤⠶⠶⠶⠶⠶⠶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⡿⠷⠶⠶⠿⣿⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⣀⡀⠀⠀⠀⢀⣤⡶⣿⠋⢿⡀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠸⠿⠟⢀⣤⠾⣯⠁⠀⠸⣧⣘⣧⠀⢀⣴⠿⠷⠶⠶⠶⠶⠶⠾⠋
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⡾⠁⠀⠙⠷⣦⣄⣈⣿⣵⡾⠛⠁
⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⢠⡟⠀⠀⢠⣶⣦⠀⠀⠀⠀⢹⡄
⠀⠀⣾⠁⠀⠀⠈⠛⠃⠀⠀⠀⠀⠘⣷
⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠃
⠀⠀⠈⠛⠻⠶⠶⠟⠛⠛⠛⠋⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡛⡛⢻⡟⣻⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠂⠀⠀⠀⠀⠀⢀⡤⢂⣤⣤⠀⠀⠀⠀⠘⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⡀⢀⢀⠀⢰⣄⡦⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠠⠄⠉⠁⠀⠀⣀⡀⠀⢠⣄⠀⠀⠀⠀⢁⠱⠍⠚⠒⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠘⠋⠀⠀⠀⠀⠸⠀⠀⠀⠀⠢⠶
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⣤⡀
⠀⠀⠀⠀⠀⠀⠤⡛⢀⠀⢀⡀⠀⠀⠈⠣⣄⠀⠑⠀⠀⠂⠀⠀⢤⣳⠂⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓⠁⢆⡀⠀⠀⠀⠉⠐⠒⠲⠒⠒⠈⠀⠀⠐⠀⠴⠇⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡄⢠⣤⡄⠀⠀⣾⡷⠀⠀⢠⣤⡄⠀⠀⠀⠘⣀⢠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠛⠊⠀⢸⡻⡇⠀⡀⢸⡆⢆⠀⠸⣟⡟⠀⣀⡀⣀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠌⠁⠀⠀⠀⠀⠁⠀⠀⠀⣾⡇⠘⡄⠀⠈⠀⠀⠙⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⡀⠀⠀⢸⣿⡿⠀⠘⠀⢀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣉⣉⣉⣉⣈⣀⣉⣉⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠊⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠠⠇
⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⠿⢿⠿⡿⢟⠻⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡿⠛⣟⣿⣿⡿⠿⠿⣿⢻⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢁⠴⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⡠⠞⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠙⠢⣈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢁⡴⠋⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠳⢄⠉⠢⣀⠀⠀⢀⡴⠋⣠⠖⢁⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠙⠦⣈⣳⠞⢁⡤⠊⡡⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡶⠋⣀⠔⢋⡤⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁⡠⠚⣡⢔⠙⢦⡈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢥⡴⢋⡠⠊⠀⠀⠙⠦⡉⠲⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡩⢊⠁⠀⡱⠃⠀⠀⠀⠀⠀⠀⠈⠲⣌⠗⠁⠬⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠊⠁⠘⠒⣁⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠐⢌⡢⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡞⡑⢄⢀⡠⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡁⠀⠀⢈⢶⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠯⠽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⡶⣴⠋⠂⠣
⠀⠀⠀⠀⠀⠀⣀⡤⢼⢀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠇⠀⢀
⠀⠀⠀⠀⢀⡜⡁⡰⣡⣤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠠⠘⠿⡒⢦
⠀⠀⠀⣠⢊⠎⠰⠁⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠊⠊⠢⠳⡀
⠀⢀⡴⠁⠂⠀⠁⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠄⠑⡙⢄
⡠⠊⡜⠀⠄⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠠⢨⠳⡀
⠑⢄⡁⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠁⠀⠃⢘
⠀⠀⠈⠓⠢⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣀⡠⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣠⣶⣯⣽⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣶⣶⣶⣶⣶⣶⣲⣶⡶⠶⠶⡶⡾⠿⣿⣶⣆⣀⣀⡀
⠀⠀⠀⠁⣇⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⡇⡇⠀⠨⡶⠋⠁
⠀⠀⠀⣇⡏⠉⠉⠉⠉⠉⠑⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠓⠒⠒⠀⠰⣇
⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣶⣶⣶⣶⣶⢶⣶⣄⠀⣶⣿⡿⣿⣷⡀⠀⠀⢀⡹⣒⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢠⡏⠀⠀⢹⡆⠘⣿⠀⢹⣿⣷⣿⣿⣧⠀⡰⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠣⣄⣀⡼⠃⢸⣇⡂⠀⢿⣿⣿⣿⣿⣇⢇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢽⣷⡘⣿⣿⣿⣿⣿⡞⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⢻⣿⣿⣿⣿⣿⡽⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡌⣿⣿⣿⣿⣿⣷⢱⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠸⣿⣿⣿⣿⣿⣧⢣⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⢻⣿⣷⣼⣿⣿⡎⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣬⠯⠭⠭⠗⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠒⠚⠙⠉⠙⠙⠒⠲⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⣤⠶⠾⠁⠀⠀⠀⢤⡠⠤⠤⡠⠄⠀⠀⠀⠹⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢹⡄
⠀⠀⠀⠀⢠⣶⠟⠇⠀⠐⠊⠑⠒⠢⠀⠀⠀⠀⠀⠔⠒⠒⠉⠒⠀⠘⠟⢷⣄⠀⠀⠀⠀⠀⢰⢻⢸⣷
⠀⠀⢀⡤⣾⠷⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠸⣿⣦⡀⠀⠀⠀⢸⣾⢸⣿⡀
⠀⠀⠸⣿⣿⣄⣀⣀⣸⡄⠀⠀⠀⢸⡇⠀⠀⠀⢀⡇⠀⠀⠀⢀⣾⣀⣀⣠⣾⣷⡟⠀⠀⠀⢸⢿⢸⣿⡇
⠀⠀⠀⠈⢿⣿⢿⣿⣿⣿⣷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣷⣶⣶⣿⣿⣿⣿⢿⣿⠋⠀⢀⣠⣶⣿⢸⣿⠀⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠉⠙⠙⠻⣯⣿⠿⠿⣿⣿⣿⡿⣿⣿⣿⡿⠿⢿⣯⡿⠋⠛⠉⠁⠀⠀⠸⠟⠛⢻⠈⣿⠀⡟⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⣤⣤⠖⠛⠛⠛⠛⠛⠉⠉⠉⠹⠛⠛⠛⠛⠳⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠤⠤⠶⣷⣤⣴⣤⣤⣤⣴⡷⠦⠤⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠘⣿⡇⠁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡇⢿⠀⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⢸⡇⢀⣿⡇⢸⣇⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⡏⡟⠏⠉⠉
⠀⠀⠀⠀⠀⢀⡤⠔⠉⡩⡤⠖⠂⢸⡇⢸⣿⣧⢸⣿⠀⠒⢤⢌⡉⠳⠤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⣀⣤⣤⣿⣇⡾⣿⠿⣌⣿⣤⣤⣄⡀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⣆⢸⠀⢸⢸
⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⡟⠉⠀⠈⠛⠀⠀⠀⠘⠁⠀⠉⢻⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⢿⠘⣦⠏⣸
⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⣧⠈⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢶⡤⢷⣤⣴⢦⡴⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⣤⣺⣟⣟⣻⣿⣿⣿⣭⣭⣽⣿⣟⣋⣀⣀⣀⣀⣐⡷⠶⠿⣗⡤⠤⢴⣻
⠀⠀⠀⢀⣀⣀⣤⣴⣶⡶⠶⠛⢻⣿⡿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠉⠁
⠀⠀⢿⣿⣿⠿⠟⠋⠁⠀⠀⠀⣿⣿⠇⠀⠀⠀⠘⣿⣿⣧⡀
⠀⠀⠘⠈⠁⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡰⠢⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠤⣠⠀⠀⠀⣀⣀⡀⠀⠢⣀⣀⠀⠀⠀⠀⠀⠘⣉⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⡩⠁⠀⠈⣉⠭⠁⢤⠉⠑⢒⠖⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢋⣄⢒⣦⡄⠀⢠⠞⠑⠦⡄⣰⠀⠀⠈⢇⣀⠴⠮⡁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠫⠤⠤⠕⠁⠀⣇⠀⡀⠤⠞⣁⡴⡖⡄⠈⠐⢢⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⠱⢄⠣⠌⠀⠀⠀⠈⠠⠄⠀⡔⠃⠁⠀⣩⠈⢫⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠏⠉⢖⠖⠒⠶⢶⠒⠒⠉⠁⠰⠯⣉⡕⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢴⠛⠒⠙⠢⣤⠀⠈⢠⡤⠚⢆⣠⠴⠯⢤⡤⢒⠏
⠀⠀⠀⠀⠀⠀⠀⠏⠉⠉⠁⠒⠒⠂⢾⡄⠀⠀⠀⣌⣛⣖⡏⠀⠀⠀⠀⠀⣠⣀⣤⠾⠋⠉⠉⢀⡐⠲⠶
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⢴⠋⠙⠻⡒⣲⣿⡇⢘⢅⣀⡀⣀⣀⣠⣿⡏⠒⠐⢰⠂⠉
⣀⣀⣀⡀⠤⠄⠀⠘⠂⠄⠠⠤⠄⢈⠓⠲⠶⠿⠿⠋⠀⢸⠀⠀⠹⡉⣠⣿⡟⠀⠠⠀⢸
⠙⡉⠉⠉⢈⠓⠒⠠⠤⠄⣀⡀⠀⠀⠀⠀⠈⠁⠀⠐⠒⠈⠳⠶⠾⠿⠟⢉⣀⡀⠈⠀⢸
⠀⢱⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠒⠤⠤⢤⠤⣀⣀⡀⠀⠀⠀⠀⢀⣀⠤⠘⠋
⠀⠘⠤⠥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠉⠑⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠀⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠒⠀⠠⠀⢀⣀⠀⠀⠀⢸⠀⠀⣀⡠⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠶⡇⠼⠆⠇⠷⠶⠰⣿⠐⠆⠸⡶⢿⡇⢼⡀⠻⠰⠶⠶⢎⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠄⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⡠⡜⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠈⣀⠆⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⣤⣤⣄⡀⡀
⠀⠀⠀⢨⠳⣩⠀⠀⠉⠈⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⡴⢒⠀⠀⠈⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢀⠸⣿⣿⣿⣷
⠀⠀⠀⠀⢱⡁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⡞⢡⠈⡆⠀⠀⠀⠘⢡⡄⠉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏
⠀⠀⠀⠀⠀⠙⢀⠀⠠⠖⠈⠀⠀⠀⠀⠀⠀⢀⠎⠀⠐⠑⣈⠟⠱⣤⡄⢦⣀⠞⣿⣖⠚⣆⠀⠀⠀⠀⠀⠀⠣⡀⠀⢼⠿⠿⠁
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠰⣦⡀⠀⠀⠀⠀⢠⢋⠀⠔⠦⢔⣻⣰⢂⣿⡄⢸⠙⢿⡙⡉⠀⠈⣆⠀⠀⠀⠀⣠⡆⠀⠔⠘⡀
⠀⠀⠀⠀⠀⠠⠌⠒⠠⠀⠙⢮⣀⠲⡤⠀⢄⠈⣃⠀⠀⠀⡼⠉⠘⠛⠣⠤⠦⠤⢯⡁⠀⠀⠈⡄⠀⢤⣾⠿⣄⠀⠂⢸⢹⠙⢦
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⣿⠂⠀⠀⠀⠈⠉⠀⠂⠓⠂⠄⠀⠁⠀⠀⠀⠀⠑⠒⠒⠊⠀⠀⠀⠻⡔⠉⠀⠀⠀⣼⠀⡼⠃
⠀⠀⠀⠀⠀⢀⡴⠶⢖⣷⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠦⠀⠠⢏⡐⠀⠀⠆
⠀⠀⠀⠀⢰⠟⠁⠆⣾⣿⠁⢉⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡠⠀⠀⣤⠀⣌⠠⣄⣀⠀⠀⠑⠦
⠀⠀⠀⠀⡞⠀⠈⡜⡏⠙⠙⢅⣀⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠈⠁⠓⠀⠀⠈⡀
⠀⠀⣰⠄⡇⠀⠀⠐⣷⣦⣴⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢠⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⠶⣤⡔⠞⢻⡥⠏⠀⠀⠀⠀⠀⢃⠈⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠒⠀⠴⠶⡄⠙⠲⠦⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠠⠤⢤⡇⠀⠀⠀⠀⠀⠀⢐⠃⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣐⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣊⣀⣀⣀⣀⣀
⣿⣿⡟⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⣀⣀⢀⣀⣀
⠀⠠⠀⠋⠋⠛⠚⠛⠛⠓⠠⠆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠂
⠀⠒⠉⠓⠀⠉⠀⠉⠒⠘⠀⠀⠀⠈⠀⠀⠀⠀⢀⢀⣙⠇⠀⢀⠢⡤⠀⠀⠀⠀⠀⠀⡀⠀⠠⠐⢀⡀⣀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠄⠡⠀⠀⠈⠉⠀⠁⠁⣤⠈
⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠠⠀⠀⠰⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢧⡄⠀⠄
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡈⠠⠌⠀⠠⡀⠀⠀⠀⠀⠦
⠀⠀⠀⣤⣀⣤⡀⣀⣀⠒⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⢀⡹⠟⠚⠛⠛⡦⠆⠀⠀⠠⠉⠀⠀⠀⠀⣴⣼⣳⣿⡶⣤⡄⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⢰⠂⠠⠤⠂
⠀⠀⠀⠀⠘⠀⠋⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⢀⡞⠀⠈⠀⠀⠀⣀⠁⠐⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢁⠻⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣄⡀⠀⠀⠀⢀⣀⣠⡤⠶⠋⠀⠀⠀⠆⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠓⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠢⢄⠀⠀⠀⠠⣀⢀⡀⡀⠀⢂⠤⣀⣠⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⠻⠟⠶⠓
⠀⠀⠀⠑⠒⠂⠀⠀⠀⠈⠀⠀⠈⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋


⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⢤⣤⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣯⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿

⢀⣏⣑⣲⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡠⠤⠤⠤⠤⢤⠤⡀⠀⠀⡗⠒⢦⡀⢀⡖⠓⢦
⢻⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠿⠀⠀⠀⠀⢸⠀⠈⠀⠀⢳⠀⠀⠉⣉⠔⠉⠙⠃
⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣷⡒⠋⠁
⠀⠀⠀⠘⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢿⡀⠀⡿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠻⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢱⠁⠀⠀⣀⣿⠓⡄⢠⡴⠖⠒⠋⠁⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣅⡀⠀⠙⣉⡰⢃⣾⣿⡀⠀⠀⢀⠠⠒⠊⠒⠄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠟⠁⣸⡇⠀⠀⡀⠀⠀⠀⠀⢈⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠁⠀⠀⠈⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠐⠤⠤⠤⠤⠤⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢀⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢗⠴⠀⢛⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⡏⣽⣛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠠⠔⠂⠈⠉⢡⠼⠉⠈⠙⠛⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⡄⣀⢀⡀⢈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂
⣶⣿⣿⣿⣷⣮⣿⣦⣶⣭⣶⣶⣶⣖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃⠁

⠬⠐⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠈⠀⠀⠹⡀⠹⠋⣳⡍⣿⡴⢿⣟⠉⡝⠀⠜⡩⠊⠰⢁⠞⠙⠁⡠⠞⠁
⢤⣄⠀⠀⠀⠀⠀⠁⠈⢢⣴⠦⠤⣤⣄⡀⠀⠀⠀⠀⢠⢖⠛⣧⣄⢸⢱⠟⠋⠀⠀⣻⡜⣁⣤⣀⣁⣀⣀⢄⣀⣤⡈⠀⠀⠀⠀⣠⣔
⣒⠠⠀⠒⠄⠀⠀⠀⠀⣟⡀⠠⢀⠤⣼⠋⠗⠓⢀⢴⢟⡀⠀⠈⠀⠚⠓⡶⠀⠀⠈⠋⠉⠉⠀⠁⠠⠏⠀⢀⠃⠀⢻⡆⡠⠐⠉
⡒⠀⠠⠤⣀⠀⠀⠀⠀⣽⠂⠀⡈⠂⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠈⠀⣀⡾⠃⠀⠀⠀⠀⢠
⠉⠛⠂⠀⠀⠀⠀⠀⠀⠈⢲⡆⠁⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠈⠠⢿⠉⠉⡧⠀⠀⠀⢘⡆⠀⠀⠀⠀⠑⠉
⠤⠄⠀⠀⠀⠀⠀⢀⡠⠤⣴⢳⡤⠀⠀⠀⠀⠀⠁⠰⠐⠀⣀⠀⠀⢢⠈⡄⠊⠁⠀⠁⠀⠀⠀⠀⠘⠃⠀⡴⠚⣫⠄
⠴⠒⠦⠤⠀⢀⡜⠉⠛⠁⠘⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠛⠉⠉⠷⣶⢦⡄⢀
⡒⠖⠂⠀⠀⣸⡏⠁⣀⠔⠚⠀⠈⠒⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣠⠟⣙
⢛⢉⡴⠎⠉⠃⠀⠸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⡷⠀⠀⠀⠀⠀⠀⠀⡀⠶
⠈⣿⣀⡀⠀⢀⠀⢀⡀⠀⢀⠀⠒⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢤⣤
⡒⡚⠻⠷⢶⣟⠀⠈⠳⢴⣎⡠⠀⠀⠀⠀⠀⠈⠀⢠⠀⠄⠆⠀⠀⠀⢀⠀⠠⠄⠈⠈⠀⠀⠀⠀⠀⠁⠀⠄⢰⡄⠀⠀⣀⣀
⢀⣀⡀⠀⠀⠘⠳⣤⣄⣀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠂⢀⠀⠀⠈⠀⠀⠀⠈⠀⠐⠄⠀⠀⠀⠀⠀⢴⢼⠁⢤⠚⠋⠉⠂⢉⣉
⠿⠁⠀⠀⠀⠀⢀⠀⠍⠁⣻⠀⠀⠀⠀⠈⠙⠉⡉⠀⡀⠀⢀⣀⡁⠀⢆⠀⠀⠈⠁⠀⠈⠉⠀⡠⠶⣤⡤⠞⠋⢀⡖⠀⠈⠐⠒⠄⠠
⠈⠀⠀⠀⡠⠂⠁⠀⢀⣴⠿⣄⣄⣡⠴⡄⠀⣠⡷⢚⠂⠀⠀⣹⡍⠂⢢⣄⣀⣤⠟⠦⠴⢧⣀⣀⣶⠏⠓⠲⠞⠋⠁⠀⠈⠀⢄⠐⠠
⣖⠔⠊⠀⠀⡠⠔⠋⠙⠁⠀⠀⠀⠀⠀⠉⠋⣱⠃⠸⣏⣠⣴⠋⢷⡄⠀⠀⢡⠇⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠁⠀⢀⡴⢋⡤⠊⢁⣀⣠⢂⡖⢠⢈⡠⠀⢰⢃⣴⣤⡌⢷⡱⢳⣧⣙⡃⢟⢉⠀⠀⠀⠁⠀⢰⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⣽⠆⠀⡀⣀⡀⠀⠷⠶⠷⠇⣀⣠⣴⣦⡀⣀⣀⠄⣤⠀⠴⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠛⠁⢀⣀⣩⣭⣤⣶⣶⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡄⢀⣼⣿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡟⣋⣉⣩⣭⡀⠀⠈⠉⠁
⠀⠀⠀⠀⣠⣶⠿⠿⣟⣚⣧⣬⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⡇
⠀⠀⠀⢰⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣻⣟⣛⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⡿⠿⠿⠟⠚⠁
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠜⠉⠁
⠀⠀⠀⠙⠛⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠁⠀⢹⣿⠀⠀⠀⢠⣖⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣯⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠻⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣤⣤⣾⣏⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠙⠛⠛⠛⠋⠉⠉⢀⡀⢀⣠⣤⣄⣰⣶⣶⣾⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⣶⣶⣆⣼⣿⠀⣿⡇⣿⡟⢹⣿⠋⢹⣿⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⠁⠿⠇⣿⣿⣸⣿⢷⣿⡇⢸⣿⠀⣾⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠺⠿⢿⣶⡆⣿⡟⢻⣿⢸⣿⠁⣾⡿⠀⣿⡏⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣶⣆⣸⣿⢹⣿⠇⣼⣿⠸⢿⠿⠿⠃⠀⠛⠃⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠛⠛⠋⠈⢉⡀⢠⣤⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣾⠂⠸⠟⠀⠛⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣈⣀⣀⣤⣀⣤⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⣠⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡿⣤⣀
⠾⣆⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⢀⡀⡀⢀⠀⡀⠳⢿⣬⣗⠲⠒⢢
⠻⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⡇⠁⠁⠈⣹⣿⣿⣿⣧⠀⠀⠛⠄⣟⠀⠀⠀⠀⠀⠀⠸⠸⠅⠧⠸⠀⠏⠗⠀⠀⠉⣴
⠀⢸⡛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠹⡟⠹⡿⣿⣿⡟⠛⢛⣿⡟⢋⣛⣛⣛⣛⠉⠉⠉⣿⣀
⠀⠈⠙⠙⠛⠛⠛⠛⠛⠛⠛⠛⡋⠉⠉⠉⠉⠉⢛⣿⢿⣿⣷⡀⠀⠡⠀⢰⣶⣶⣿⣿⣿⣿⣿⣧⠭⠭⠭⠵⠀⢠⣾⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣛⠿⠛⠛⠻⢿⣿⣿⣿⣿⣷⡻⡉⠋⠐⠤⠄⠤⠤⠂⠊⢏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⣆⡟⠀⠙⣿⣷⡘⡀⠄⢑⢀⠠⡠⠂⠰⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⣴⠙⠁⠀⢀⣿⣿⡇⢱⠀⡀⠀⠀⠈⠂⠀⠉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠶⠖⠚⠁⠈⠙⢾⡎⢊⠂⠐⠐⠄⠀⡠⡀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡌⣆⠀⡀⠠⠀⠈⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠘⡈⠪⠀⠀⠔⠅⠌⠠⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⢡⠀⠀⡠⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡈⡆⠀⠂⠢⠀⠀⠕⠄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⠀⠀⠀⠀⡀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⣨⣀⣁⣀⣀⣊⣂⣀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡵⠊⠁⠖⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⠀⠀⠀⠀⠹⡂⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣄⡣⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⠀⠀⠀⠀⠼⡙⢄⠰⠂⠢⡀⠀⡠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠀⠀⠀⢠⣇⠈⠲⢇⠀⢘⡎⠠⢠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⠀⠈⠄⢸⡻⡾⠼⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠠⠀⠀⠀⠀⠀⡸⡀⠀⠘⢤⡋⢸⠉⠁⠒⠂⠒⠒⠒⠒⠒⢠⠀⠀⠀⠀⢠⢆⡠⡀⣀⡄⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠋⠀⡜⠁⠒⠀⠤⠄⠐⠊⠁⢀⡤⠂⠀⣐⡉⠉⠁⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⣠⠄⠀⠀⠀⠀⠑⡎⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⣤⠋⠀⠀⠀⠯⠙⠋⠱⠎⠟⠶⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⢶⣀⣸⠑⢆⡔⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡣⠊⠀⢀⠔⠊⠁⠀⠀⠀⢀⣠⠄⡀⠀⡀⠉⢘⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⢄⠰⡖⣉⠀⠀⠀⠀⠀⠠⠋⠉⠁⠒⠠⠌⣥⣤⣸
⠀⠀⠀⠀⠀⠀⠀⠠⡄⠐⢛⠔⡰⠂⠘⡄⢡⠱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣠⠃
⠀⠀⠀⠀⠀⢀⠄⠊⠳⣀⠊⠎⠀⠀⠀⠘⣸⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⡴⠠
⠀⠀⠀⠀⠀⡄⠀⠀⠀⡏⢸⢠⠀⠀⠀⠀⢸⢱⠐⠂⠰⢣⠄⠤⢄⣀⣀⡎⠁⠉⠃
⠀⠀⠀⠀⠀⠇⠀⢴⠉⠂⠁⡉⠈⠒⠀⡤⠴⠈⠉⠀⠉⠉⡀⠀⣀⠃⠈⠐⠒⠂
⠀⢀⠀⠀⠰⠀⠀⠀⠥⠐⠊⢁⠀⠀⣰⡿⡟⠀⠀⠀⠀⠀⠓⠐⠒
⢠⠏⢃⣤⠊⠀⠀⠀⠖⠀⢀⠘⠀⡰⢟⠹⠁
⣼⣀⡮⠽⠁⠀⠀⠀⠈⠁⠀⢀⠌⠀⠎⡀
⡇⠀⠁⠀⠀⠀⢀⡠⣻⠋⠀⠇⠦⠚
⠣⡠⠀⠀⠀⠶⠭⢔⣁⠀⠈⠉⢐⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⢄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⠤⠈⠀⠀⠀⠀⣀⣀⣀⣀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢁⡾⠤⠒⠒⠚⠛⠛⠓⠒⠒⠤⢄⡀⠉
⠀⠀⠠⢤⡀⠀⠀⠀⠐⠢⠄⣸⢀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⡐
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠉⠒⠤⠤⠒
⠀⠀⠀⠀⠀⢱⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠠⠐⠈⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣠⠒⠁
⠀⠐⠓⠲⠄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠙⢦⡀
⠀⠀⠀⠀⠈⠢⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⢤⣀⣀⡄
⠀⠀⠀⠀⡠⠔⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠜
⠀⠀⢠⠊⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣀⠀⠄⠂⠁
⠀⢠⠇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⡄
⠀⠸⠈⠁⠉⠐⠠⢀⣀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠔⠂⢙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡈⠀⠈⠙⠲⠦⢤⣀⣀⣀⣀⣀⣀⣤⡤⠖⠋⠁⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣀⠤⠚⠩⡀⠀⠀⢀⠞⠉⠢⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡴⠋⠁⠀⠀⠀⠀⠑⢄⡀⠏⠀⠀⠀⠈⠑⠒⠠⠵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢉⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣄⣠⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠉⠁⠉⠳⡌⠛⡵⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣀⣀⠀⠀⢀⣀⢹⢀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠉⠀⠀⠈⠉⢸⢹⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⡀⠀⠀⡤⠄⠀⣸⣿⢿⢰⡇⠀⠀⠀⢻⣯⡉⠙⡄⠀⣸
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡴⠁⢉⢻⣲⢶⣺⡏⢯⠀⢸⣸⠁⠄⢀⢀⡀⢷⢧⠀⠘⣄⡏
⠀⠀⠀⠀⢠⠏⣅⠀⠀⠀⠀⡼⠁⠀⠘⣧⣠⡏⡽⣧⢸⡆⢀⣉⡓⠒⠒⠒⠒⠚⢯⢧⠀⠈⢧
⠀⠀⠀⠀⠘⣆⢹⠀⠀⠀⢰⠇⠀⠀⠀⠈⡿⣧⣇⣈⣿⠷⠯⠽⠿⠦⠼⠯⠭⠭⠭⠤⠧⠤⠬⠧⠤⠤⠤
⠀⠀⠀⠀⠀⠈⠙⠒⣶⠲⣿⠀⠀⠀⠀⡸⠁⢧⡏⠀⠓⠒⠶⠶⠶⠶⠶⠶⡶⠶⣶⠶⠶⠶⠶⠶⠶⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣚⣿⡆⠀⠀⠀⠳⣤⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢠⠇
⠀⠀⠀⠀⠀⠀⣠⢖⣛⡛⠛⠛⢦⣠⣤⣀⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠙⠦⢬⣭⣭⣀⣀⣈⣽⣿⡏⡿⡒⢢⠀⠀⣠⣤⣤⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢻⠀⠀⢸⣿⠏⢀⣾⣠⡿⠋⢁⡼⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⡞⣩⣟⠛⠛⠛⢯⡝⣤⣿⡠⠊⠘⠯⠴⠚⠉⠀⠀⢀⣀⣸⣸⣀⣀⡀
⣀⣀⣀⣀⣀⣀⣀⣯⣥⣞⣀⣀⣀⣸⣮⣽⣁⣀⣀⣀⣀⣀⣀⣀⣀⣾⣥⣤⣤⣤⣤⣤⣭⣷⣄⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠢⣄⡈⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣀⠤⣤⡀⢀⡀
⠀⠀⠀⠀⠀⠙⠳⡂⢌⡛⢶⠤⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠉⠳⡃⠀⡤⠚⠉⠉⠲⣄⠀⠀⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⡀⠈⠲⢌⠉⠓⠊⠙⠳⡴⠚⠓⠶⠉⠈⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⡇⠀⣀⠤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣦⡽⠄⠀⠀⠀⠢⣄⠀⠀⠀⠀⠈⣇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠗⢋⣵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⢿⠄⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡙⠦⡼⠘⢤⠃⡇⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢳⡆⠀⠀⠀⢀⣠⣤⠿⠀⠀⠀⠀⠀⠉⢹⣃⣀⣤⣤⠶⠚⠉⠀⠀⠀⠀⠰⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⢈⣉⡷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣁⣀⠀⠀⠀⠀⠀⠀⣠⠤⠬⠅⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠆⠀⠀⠐⠒⠛⠻⠶⡄⠀⠀⠀⠀⠀⠀⠀⡤⢝⣷⣌⡉⠁⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠥⢄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠈⠉⠓⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⠔⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⣴⣴⡀⣶⣾⡁⠚⠆⠀⠀⠀⠀⠀⠀⠀⢺⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠏⠘⠇⢷⡏⠃⠙⠀⠀⠀⠀⡔⠢⠤⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⣀⣴⡯⠴⠒⣞⠉⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠙⠒⢄
⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠙⠢⢤⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⡤⠖⠁⠀⠀⠰⣕⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣖⠚⠁⠀⠀⠀⠀⠀⠀⠁⠠⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢲⣶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⡏⠹⡄⠀⠀⠀⢀⡄⠀⠀⠀⡇⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡘⠀⠀⠉⠓⠒⠚⠁⠘⠦⠤⠞⠁⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠰⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠐

⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣾⣿⣶⡀
⠀⢰⠆⠀⠀⠀⠀⠀⠹⣿⠀⠀⠄⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠠⠀⢰⠆⠀⠀⠀⠀⠁⠠⣶⡿⠁
⠀⠘⣦⡀⠀⠀⠀⠀⣠⠟⠀⠀⠈⢃⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⢀⠉⡼⠁⠀⠘⣦⡀⠀⠀⠀⠀⣠⠟
⠀⠀⠈⠙⠺⡤⡴⠚⠁⠀⠀⠀⠀⠈⢳⣴⡿⠁⠀⠀⠀⠠⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠘⢾⢿⡞⠀⠀⠀⠀⠈⠙⠺⠤⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⡉⠁⣀⡀⢊⠀⠰⠉⠀⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⢿⡟⠚⠖⠁⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠁⠘⠀⠀⡃
⠀⠀⠀⠀⠀⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣤⣾⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆
⠀⠀⠈⠐⠒⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠈⠐⠒⠒⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠰⣄⣀⠀⠀⢀⣠⣶⠾⠼⢶⣤⣤⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢄⣽⣷⣶⣾⣿⣟⣥⣄⠀⠀⠈⠛⠻⢷⣄⡀⢤⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣷⣽⠏⠁⡦⠊⠀⠀⠀⠀⠀⠀⠈⢲⣾⣿⣏⣴⡙⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⡄⠀⠀⠀⡠⠔⠚⠓⠒⠄⠀⠈⠙⠍⠙⢿⣧⣤⣤⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠐⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⠁⠉⠲⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠻⡀⢠⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡦⠀⠀⠀⠀⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⢀⣦⣼⣧⡑⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣭⣾⣷⣄⢀⡀⢤⣠⢤⡀⠀⠀⠀⡠⠀⠀⠐⢺⣿⠁⠈⠉⠓⠤
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠈⢦⣙⠿⠿⣿⡛⣆⣈⣉⣙⣳⣶⣍⣂⣀⣠⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠁⢈⠛⠻⠿⠛⡋⠉⠺⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠛⠛⠉⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⡭⠭⠭⠭⠭⠭⠭⠭⠭⣽⢃⣀⣀⣀⣀⣀⣀⣀⣄⣏⢧⣿⣤⣤⣤⡤⠿⠛⢛⣛⡃⣀⣀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⣇⣸⣿⡆
⠀⢀⠈⠉⠁⠉⠉⠉⠁⠀⠉⠉⠈⠉⠉⠉⠉⠉⢿⠙⠉⠉⠁⠈⣹⢩⡽⢻⡟⣡⣤⣬⣭⣭⣭⣍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣾⣿⣿⣿⠃
⠀⠈⣳⣄⣀⣀⣴⣷⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣾⠗⠋⣀⡾⠁⣋⣁⣠⣉⠉⢉⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⣿⣿⣿⡟
⠀⠘⣷⣈⡛⢻⡿⣯⡆⣿⣦⠀⠀⠀⡆⠀⠀⠀⠀⣯⠲⠶⠶⠶⠶⣾⠟⠛⠻⣿⡿⣿⣿⣿⡶⠾⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⣿⡷⣿⡍⢱⣧
⠀⠀⣧⠻⢿⣿⡿⣝⣧⢸⣿⣆⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠠⣽⣧⠀⠠⠶⠖⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢸⡿⣧⣿⣿⣧⣿⣧⣼⣹
⠀⠀⢿⣏⡞⣾⣷⣿⡞⢆⠻⣿⡄⢸⣿⠀⠀⢀⣀⡄⡤⣞⣭⣿⡇⠀⠀⠀⠀⢘⣿⣆⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢀⠤⠒⢏⡁⣿⣿⣿⢸⣿⣻⣿⣿
⠀⠀⠪⣼⢸⣿⠗⣶⢭⡛⡇⢹⣿⣿⣿⣿⣿⣿⣷⡷⣿⡿⠻⣿⡇⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⣻⡆⠀⠀⢧⡀⠀⠈⣷⣿⣿⣿⢸⣿⢼⣿⣿
⠀⠀⢸⢣⣾⣿⡜⣿⣥⣽⢀⠀⣿⣿⢿⡟⠛⠁⢹⡧⢿⠃⠀⢹⡇⠀⠀⠀⠀⠀⠹⠿⣿⡶⣿⣿⣿⣿⢿⠟⠃⠀⠀⡀⠳⠦⣼⡏⣿⣿⣿⢉⢹⣺⣿⢾
⠀⠀⣿⢸⣿⣿⣿⢡⣥⣸⢸⣇⢸⣇⣘⣻⣆⢵⠌⠴⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠳⢀⠠⠟⠁⣿⣹⣿⣎⣘⣿⣿⢿⡀
⠀⠀⣿⡈⣿⣿⣿⡠⣿⣿⡆⣿⣿⣿⢹⠙⢻⣖⡶⠲⠒⠒⠂⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣋⣽⠶⢤⣀⠀⠀⠀⠀⠀⠈⢢⢊⢏⢩⣿⣿⡟⢩⣍⡾⠇
⠀⠀⣿⢰⣿⣿⣿⣷⣜⢶⣄⣿⣿⣿⡉⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣮⡿⡿⣎⡽⢳⡦⣤⣤⡴⣫⣤⣼⣸⣿⣽⣵⣰⡿⠃
⠀⠀⢻⡎⣿⣿⢟⣿⣿⣷⣽⣿⣿⡏⠁⠀⠀⠀⣤⠴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣵⡟⣈⠇⣼⣇⣬⠒⢛⣮⠷⣼⡿⣿⠛⣹⣿⡀
⠀⠀⠋⣿⣹⣷⣏⣴⣿⣿⡿⣿⣿⣶⠀⢠⡎⡘⠀⢛⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⢋⢹⡕⢿⠓⣷⣼⢨⡇⣶⣶⡉⢯⣽⣷⠟⠀⢻
⠀⠀⠀⢸⣿⣯⣻⣿⣿⣿⣽⣿⠏⠀⠀⣿⡇⠃⢠⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣿⡿⣭⠾⠶⠾⠏⠚⠛⠉⠉⠉⠛⠳⠿⠀⠀⠈
⠀⠀⠀⠀⠻⣿⣯⠙⣛⣭⣿⠏⠀⠀⠀⣿⠇⢦⡀⠉⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⠶⠶⠶⣤⡀
⠀⠀⠀⠀⢠⣿⣿⡇⢻⣷⣿⡆⠀⠀⠀⢹⡀⠀⣸⡲⡀⠀⢜⢿⡄⠀⠀⠀⠀⠀⢀⢮⠋⠀⢾⠀⠀⠀⢨⡗
⠀⠀⠀⠀⠈⢻⣿⡄⢠⣿⣿⠃⠀⠀⠀⠈⢧⡀⠸⣷⡈⠀⠀⠈⠻⣦⣀⠀⠀⠀⡨⣾⡀⣠⣎⣻⣦⣴⢟⣥⣴⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠐⢿⣿⣇⢀⣿⣯⠇⠀⠀⠀⠀⠈⠳⣦⣬⣉⠳⠀⢄⠀⠩⠝⠟⡿⢡⣤⣤⢥⡄⢤⣤⣴⡆⢸⣿⣿⣟⣘⣛⣋⣙⣟⣛⣓⣆⣐⣂⣐⣲⣰⡃
⠀⠀⠀⠀⠀⠀⣿⠃⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠰⣦⣔⡠⡄⢠⡇⠷⣿⣽⣯⡟⣾⣷⣿⡇⢿⠿⡟⣟⢹⠋⠉⠉⢉⢉⠙⠋⢉⡙⠋⠛⠛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠀⣀⣠⣤⣬⣥⣤⣄⣀⠀⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡦⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢴⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠾⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠈⠉⠛⠛⠻⠟⠛⠛⠉⠁⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠉⠉⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡔⠀⠙⠀⠂⠀⠀⠀⠀⠈⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⡃⠊⠀⠀⠀⠀⠀⠘⠀⠈⠁⢀⠡⠏⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠓⠀⠿⢂⢠⠖⠄⠘⠟⡀⠔⠁⠀⡀⠌⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⠠⠤⠄⠠⠤⠀⠤⠤⢴⠀⠀⠀⠀⠣⡀⠀⠁⠠⠀⠀⠀⠀⠀⡰⡀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠈⠢⢀⡀⠀⠀⡀⠀⢊⠂⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠄⠠⠀⠤⠀⠀⠘⠀⠀⠀⠐⠀⠀⠀⠀⠇⠄⠀⠀⠀⡠⠃⠂⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠧⠄⠤⠤⠤⠤⠤⠤⠤⠤⠴⠤⠀⠀⠀⠀⠀⠀⠀⢈⠠⡀⠇⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠩⠀⠀⠀⠘⡛⠛⠻⠀⠀⠀⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠂⠈⠛⠀⠀⠄⠀⠀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠡⠀⠀⠈⠄⠀⠄⠈⠀⠀⠀⡰⠀⠀⠀⠈⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠲⠦⡄⢀⠀⠀⠀⡄⠒⠐⠂⠢⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠐⠀⠀⠘⠀⠘⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠉⡙⠉⠋⢂⠈⢂⠀⠀⢀
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠑
⡔
⠧⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠟⠋⠀⣀⣤⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⠛⠁⢀⣠⣴⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡿⠟⠋⠁⣀⣤⣶⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡿⠛⠉⢀⣠⣴⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣧⣀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠁⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣶⣿⣿⠃⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⣿⣿⣿⣿⣷⣄⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠛⢿⣄⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠙⠛⠷⠶⣂⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣀⣠⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠻⣿⠇⠀⠀⠀⠸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢀⣠⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⣀⣴⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠟⠉

⢿⣍⣉⣉⣉⣉⣉⣉⣹⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⠋⢹⠉⢹⡟⢾⣝⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣸⣇⣞⣠⠟⢉⣷⣻
⠀⠀⠀⠀⠀⠀⠀⠘⢯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⣛⣉⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣠⣾⡿⣭⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⠜⠁⠈⢿⢦⣈⡽⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡤⠉⠀⠀⠀⠈⠳⣟⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣠⠎⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⢻⣿⣿⣿⣿⣿⣿⣿⡿⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠙⢿⣿⣿⣿⡿⠋⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠛⠛⠛⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠂⢲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠀⢸⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠚⠋⠉⠉⠁⠀⢹⣀⣸⠀⠈⠉⠉⠉⠓⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠿⠃
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢤⣴⠲⠃⠀⠀⠀⠀⢀⣴⣾⣿⣷⣦⡀
⠀⠀⠀⢠⠾⠿⠿⠿⠿⠳⡄⠀⠀⠀⠀⣹⣿⣶⣦⡀⣿⠀⠀⠀⣀⣀⣾⣄⣀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⣿⡇
⠀⠀⠀⡎⠀⣀⠀⠀⣀⠀⢹⠀⠀⢺⡏⠉⢩⡤⣿⣿⣿⠀⠀⢸⣯⣿⣿⣿⣯⣷⣄⠀⠀⠀⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠘⣄⠀⠰⠆⠀⣠⠏⠀⠀⣼⠀⠀⣾⠁⢉⢏⡉⠀⠀⠘⣿⣿⣿⣿⣿⠷⠊⠀⠀⠀⠘⠻⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠙⠒⠒⠋⠁⠀⠀⠀⠙⠂⠀⠁⠀⠃⠀⠓⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⡖⣴⣶⠉
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⠖⠚⠉⠀⠉⠣⣄⠀⠀⠀⠀⣴⣿⣿⣶⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⢰⠄⠀⣠⣽⣿⣄⠀⠀⠀⠀⡼⠀⣽⠡⡤⣰⠀⢸⡀⠀⠀⠰⠏⣿⣿⠘⠇⠀⠀⠀⠀⢸⡁⠀⠀⢸⣿
⠀⠀⢸⣦⣤⣧⣿⣿⣼⣤⣤⡆⠀⠳⣤⡉⠘⢃⠉⢀⡞⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⡄⣠⠠⠀⣠⡀⡄⢠
⠀⠀⠸⠋⠉⠉⠯⠹⠋⠉⠉⠇⠀⠤⠋⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠿⠸⠇⠀⠀⠀⠀⠁⠉⠀⠀⠈⠁⠉⠈
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠱⠝⠆⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠻⠻⣿⡆
⠀⠀⠀⢲⣶⣶⡶⡖⣶⡦⣄⠀⠀⠀⠀⠻⣿⣿⡃⠀⠀⠀⢠⡄⠀⣹⠃⡤⣰⠂⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠘⣿⣑⣷⣿⣿⠷⠋⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⢸⣧⣤⣤⣬⣧⣬⣤⣄⡆⠀⠀⢻⣿⣿⣿⣿⠋
⠀⠀⠀⠠⣬⣽⣿⣯⣥⡄⠀⠀⠀⠀⠀⠀⠿⠸⠇⠀⠀⠀⠸⠏⠉⠉⠉⠉⠉⠉⠉⠇⠀⠀⠀⠀⠿⡿⠿⠆
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀
⠀⠀⠀⠀⠀⢴⣿⣣⡀⠀⣿⠀⠀⠀⠀⠀⣤⣶⣄⠠⠀⠀⠀⢀⣤⣶⣿⣿⣶⣦⡀⠀⠀⠀⠀⣰⣿⣿⣶
⠀⠀⠀⣠⡤⠾⠿⣙⣿⣦⣿⠀⠀⠀⠀⠘⢿⣹⡟⠀⠀⠀⢀⣿⠿⠟⠛⠁⠀⠙⢿⡆⠀⠀⢠⡏⣿⣿⡟⡇
⠀⠀⠀⣿⠁⠀⣸⠏⠽⡿⠿⠀⠀⠀⣠⣶⣿⣿⣷⣦⠀⠀⢸⣿⠀⠒⢃⡀⠒⠀⣸⣿⠀⠀⠀⠀⣿⢹⡇
⠀⠀⠀⢿⡀⠀⠏⠀⡔⠁⡆⠀⠀⠠⣿⢸⣿⣿⣿⠿⠇⠀⠸⠿⠷⠤⣈⣁⡤⠾⠿⠏⠀⠀⠀⠀⣿⢸⡇

⠀⠀⠀⠀⣀⣀
⠀⠀⠀⣸⣿⠈⠉⠓⠲⢤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⡖⠒⠒⠒⠶⠶⠶⠦⠤⢤⠀⣀⣀⣀
⠀⠀⢀⣿⠿⣀⣛⣛⣋⣓⣒⣐⣀⣀⣂⣀⣀⣀⣂⣀⣀⣀⣀⣠⣦⡼⢧⡤⠘⢿⣛⣛⣻⣟⡷⠈⢛⣡⣶⠿⠃
⠀⢠⣿⢿⡝⡖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣷⣀⣸⣦⣀⣀⣀⣁⡀⡌⢿⣁
⠀⠘⣿⣌⣋⣿⣶⣶⣶⣶⣶⣶⣶⡾⠿⠿⠿⠿⠿⠟⠛⠛⠛⣛⣿⣭⢻⡯⠉⢻⣿⠿⠿⠟⢻⢿⠖⠂⠈⠉⠳⡀
⠀⠀⢨⣿⣿⣜⠛⠒⠉⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣶⣶⣶⣶⣟⣼⠷⠶⣾⣿⣀⣠⣤⣤⡞⠀⠀⠀⣴⣷⡳⡄
⠀⠀⠘⣿⣈⢿⣴⣶⣶⣶⣶⡿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠈⣿⣧⠀⠛⠛⢛⠋⠉⠉⣠⣤⡄⣸⣿⡿⣿⣿⣆
⠀⠀⠀⠈⠙⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣧⣶⣼⣿⣿⣧⢰⣿⠋⣷⣿⣿⣿⢿⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⡌⢿⣟⣼⡇⢠⢿⣿⣿⣿⣗⡾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⠭⠽⠒⠉⢸⣿⡿⣿⣷⢽⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠃⣿⣿⣯⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣿⣿⡿⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣠⠴⡏⠀⢘⡦⢤⣀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠀⠀⠙⢢⡴⠚⠁⠀⣳⠖⠛⡇⠀⠈⢳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡄⠀⠀⣞⣉⡀⠉⠳⣄⡠⠃⣠⠴⠋⢱⠀⠀⠹⣄⠀⠀⢻⡀
⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠲⠦⣄⠀⠀⠀⢀⡴⢚⣵⣿⠟⠁⢀⡖⠉⠉⠉⠳⡤⢃⡴⠚⠁⣀⡀⠈⢳⡀⠀⠈⠳⣄⣸⠇
⠀⠀⠀⣠⠖⠛⠀⠀⠒⠤⡀⠀⠈⢳⣤⠞⣩⣶⣿⠟⠁⠀⠀⣈⡿⠓⠦⢤⡾⠞⢉⣤⣤⣞⠉⠉⢳⡄⠙⢦⣠⠴⠊⠁
⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠈⢢⡴⢋⣤⣾⣿⡿⠃⠀⠀⠀⡞⠁⠀⣠⠖⠛⣆⣠⡏⠀⠀⠈⢳⡄⠀⢿⠴⠋⠁
⣰⠃⠀⢠⠀⠀⠀⠀⠀⣀⡴⣋⡴⠿⣿⡿⠋⠀⣀⣀⣀⡴⢧⡴⠋⠁⠀⡾⠉⠈⠉⠳⣄⠀⠀⡇⠀⣿⣀
⣏⠀⠀⠀⢢⠀⠀⣠⠞⣡⠞⠁⠀⠀⠀⠙⠶⣼⡏⠉⣇⠀⣻⠀⠀⠀⠀⠙⢦⡀⠀⠀⢘⡆⠀⠛⠁⠀⠉⢳⡀
⠹⣤⠔⠀⡀⣱⢞⡥⠾⢥⣀⠀⠀⠀⠀⣴⠀⠈⣷⠶⢾⠋⠉⢧⡀⠀⠀⢀⣠⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠈⠓⢮⣞⡵⠋⠀⠀⠀⠈⠙⣆⠀⠀⠇⢀⠋⢹⡀⠘⣆⢀⡤⠛⠲⠖⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠤⠶⣏⣀⣀
⠀⠀⠀⢰⠏⠀⠀⠀⡘⢦⠀⠀⢸⡇⠀⠀⠈⣄⠀⠳⣄⡀⡾⠀⠀⠀⠀⠀⠀⣹⠶⠤⠤⠔⢿⣠⠴⠚⠋⠉⠉⠙⢷⡀
⠀⠀⠀⢿⣤⢀⠀⠀⠙⡄⣇⡀⠈⡆⠀⠀⠀⠈⣓⡀⠘⠉⠁⠀⠀⠀⢀⣠⢾⡉⣧⠀⠀⣴⠋⠁⠀⢀⣀⡤⠴⠖⠚⣧
⠀⠀⠀⠈⠙⠾⢄⠀⡴⠋⠉⠈⠙⠃⠀⠀⠀⢋⣭⡥⠀⠒⠒⠒⠒⠉⠉⠀⠀⢳⡸⡆⠸⣇⢀⡤⠚⠉⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⠴⢦⣄⠀⠀⠀⠀⠀⢹⡉⠲⣄⣀⣀⣀⣠⠴⠊⠀⠈⣇⣷⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠁⠀⢀⡄⠀⠀⠀⠀⠳⣤⣤⣤⣴⣿⠤⣤⣀⠀⠀⣿⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠔⠖⢻⡄⠀⠀⠀⠀⠀⠈⠻⠯⠤⠴⠋⠉⠉⠀⠀⡿⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡾⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠛⠚⠋⠉⠉⠉⠉⠙⠛⠓⠒⠶⠤⣄⣠⠏⣸⠃⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⢉⣉⣵⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠘⠋⠉⡽⠀⡇⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠚⠁⡼⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠴⠊⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢳⡀⠀⠀⡇⠀⢸⠃⠀⢀⠞⠁⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠐⢄⠈⢢⠀⡀⢣⠰⠀⡇⠆⢏⠄⣠⠋⠀⣠⠖⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣀⠀⡑⢄⠑⠌⠀⠂⠀⡇⠘⠌⡔⡡⡢⠞⢁⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⡀⠁⡂⠀⠀⠀⠀⣀⠀⠁⠀⠪⡈⢀⠠⢚⡡⠀⣀⡤⠴⠂
⠀⠀⠀⠀⠀⠰⠶⠦⠤⢤⣀⣀⡉⠑⠀⠀⡐⢡⠊⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢉⣀⣠⣄⣠⣤⡴⠒⠦⠤⠴⠒⠶⠄
⠀⣀⣀⣀⣀⡤⠴⠤⠤⠤⢄⡀⠀⠄⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣁⠀⣀⠴⠉⠉
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⢄⣀⣀⠨⠤⠤⠤⠤⠔⠊⠉⠀⠀⣀⠜⢁⡤⠂⠀⠐⠀⢀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠁⠐⠄⠄⠀⣀⠐⠄⠀⠀⠵⢦⣒⠂⠀⠀⠐⠒⡴⠊⢉⠁⠂⠉⠀⠶⠀⣒⠍⣁⣀
⠀⠀⠒⠐⠒⠐⠀⠐⠂⠐⠒⠀⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⣰⠚⣡⣀⣄⣖⡰⠀⠀⠂⠁⠚⠀⠘⠲⠗⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⢤⣭⠴⠞⠟⠋⣁⣉⠁⣀⣈⠛⠛⠛⠋⠉⠉⠓⠒⠛⠛⠚⠓
⠀⠀⠀⠠⠶⠒⠒⠛⠒⠛⠓⢾⣍⠉⠁⠀⠩⠤⠬⢒⣐⠈⠁⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠀⠰⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⣮⢳⡐⡄⠀⠀⠀⠀⠀⠀⡄⣾⠈⢁⡀
⠀⠀⠀⠀⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣷⣧⢳⡀⢀⣤⣤⣤⣀⣷⡸⢀⣾⡇⠀⠀⢀⣶⣮
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣸⣿⣟⣷⣿⣿⢟⣛⣿⣿⣷⣼⣿⣷⣶⣷⣿⣿⣃⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⢹⣶⣾⣿⣿⣿⡿⢿⣾⣿⣿⣷⣿⣿⣭⣿⡿⣹⣿⡟⠁⠀⢀⠍⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢦⣤⣄⠀⠄⢘⢓⣏⠀⣠⣿⣎⣻⣿⣿⣿⣿⣯⣭⣻⡿⣿⣿⣿⡿⠉⢰⣿⣏⣤⠀⠀⠈⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⢿⣷⣷⡦⣈⠁⠀⣾⡟⣛⢛⣿⡿⡿⣿⣟⣭⣽⣷⣶⣾⣿⣡⠀⠈⢿⡿⣿⣾⣶⣶⣀⣀⠈⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠺⡦⠀⠀⠀⠀⠀⠀⠉⠳⢶⣦⣝⣲⣿⣿⣁⣿⣿⣿⣿⣯⣹⣿⣿⣽⠛⠛⢿⣧⣎⣴⣿⣷⣹⣿⣟⣿⣿⣿⣿⣾⣵⣿⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⣿⣿⣿⣿⣽⣿⣿⣭⣿⠏⠀⢿⡛⠩⠀⠀⠘⠃⣸⣷⣍⢻⣟⣮⢻⣼⣿⠿⠛⢋⣉⣤⣴⠂
⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠁⣀⣿⣿⣿⣿⣿⣿⠎⠋⢐⡂⠈⠐⢶⣶⠄⠘⣧⣽⣭⠛⢻⡟⢛⣉⠭⠔⢒⡈⠉⣉⠡⠤⠴⠶⡂⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣼⡿⣽⣉⣿⣿⡿⡿⠆⣐⣿⠀⠀⠀⠀⠁⠀⢀⡿⢿⣿⠀⣠⢫⣧⣶⣾⣿⣯⣭⣶⣶⠖⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠀⣤⣾⢠⣿⢧⢸⣿⣿⣟⢷⣿⠀⠙⠁⠀⠀⢠⣾⣧⡤⠉⣠⣾⣷⣦⣭⡾⢿⡿⣿⣟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠉⠀⠀⠁⢼⣿⣿⣎⣻⣿⣿⣾⣿⣦⡀⣀⠴⠆⣼⣿⣿⡠⠐⠋⠻⠻⢿⣟⣱⡏⣶⡏⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⣽⣿⡿⠻⠛⠛⢉⣨⣿⢇⠈⠉⠁⣩⣿⣿⠿⠛⠀⠀⣠⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡿⣦⣤⣠⣶⡿⣿⣿⣟⡷⣶⣿⣿⣏⡀⠀⠀⠓⠘⢿⣿⡿⠁⣸⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡴⠟⠉⡈⣩⣴⢿⣿⣧⣽⢷⣼⡿⣿⣿⣤⣬⣽⣻⣿⣎⡓⡄⠀⢈⡻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠉⠁⠀⠉⠹⠿⢷⣽⠶⠾⠿⠿⠿⠿⣿⣿⣿⣿⡿⣆⠢⡹⣿⣧⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠟⠀⠀⠀⠀⡈⠀⠀⠀⠙⣧⢻⣎⠻⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢻⣆⠈⠁⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠿⡻⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⠉⣨⣴⣿⣿⣿⣿⣿⡟⢿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣷⣶⣼⣾⣷⡟⢩⣿⣿⣿⣛⢛⣭⣿⠎⣉⡠⢧⡃⠉⢻⡆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⣟⣟⣭⣭⣽⢻⣬⣷⣾⣿⣿⣿⣿⢿⣿⣿⣿⣭⠤⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠞⠁⢁⣬⣶⣿⣿⣿⣿⣿⢿⣯⢿⣿⢿⣿⣿⣦⡥⢿⣿⢿⣿⣿⣿⡿⠒⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⡟⣼⣿⣿⢿⣹⣿⣟⣻⣿⢹⢿⣿⣿⣿⣿⢸⢻⣿⣿⣷
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠷⣼⣿⣿⣿⣆⣻⣿⣿⣖⢿⡜⠘⠏⢹⣿⣿⣌⡀⠀⠹⠛
⠀⠀⠀⠀⠀⣼⠿⠟⠏⠈⢠⣿⣿⡝⠯⡧⢹⣿⣯⡓⠸⣷⠀⠀⠏⢿⢿⡓⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⡿⡝⠆⠀⢸⣿⣦⡉⠀⣿⢀⣤⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠑⠈⠀⠀⠀⠻⠇⣩⣶⣿⡝⢿⣿⡿⣶⣤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⡿⣫⠵⢿⣹⡇⠀⠀⠹⡄⢹⠷⠄⠀⣀⣙⠿⣔⣲⣤⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠛⠛⠛⣿⣷⣾⣖⣲⣤⣄⣿⡗⠛⠛⠓⠂⢲⣶⡼⠶⢦⣸⣷⣶⡿⠿⠿⠿⠛⠛⠛⠻
⠀⠀⠀⠀⠛⠉⠛⠒⠒⠒⠚⣁⣤⣤⠤⠤⠌⠈⠉⠒⠒⣿⡇⠉⢁⣷⡆⢠⠈⣡⠈⣋⣉⣣⠤⠴⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⡾⢸⢻⢃⣮⢞⢥⠀⠠⠤⠭⣭⣿⣿⣯⣈⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣬⡏⢀⡟⣯⣈⣬⡃⢻⣾⣯⣀⠀⠐⣾⠿⠿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠒⠊⠉⢛⡽⠋⠋⠀⠸⠘⠹⠉⠳⠈⠙⠛⠿⠿⢽⣿⠿⠿⠓⠒⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐
⠀⠀⠀⠄
⠀⠀⣠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠒⠂⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠐⠤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⡠⠙⠖⠶⣤⡒⠶⠞⣛⠇⠀⠄
⠀⠀⠀⠀⠀⠀⠆⢰⠀⡄⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⠃⠀⠀⠐⠂⠀⠱⠀⠀⠈⡃
⠀⠀⠀⠀⠀⡔⠀⠠⣀⠏⠂⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⡀⠀⢀⠀⣇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠀⠀⢀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡝⠉⡻⠉⡆⠣
⠀⠀⠀⣶⣤⠉⠉⢻⠀⣶⣀⣀⣤⣟⣀⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢐⡄⠁⢀⣄⠀⠀⠄
⠀⠀⠀⠻⠿⠿⠒⢿⠀⣽⣿⢿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣿⣷⣿⣟⣀⠠⠀⠠
⠈⠁⢰⠀⠀⠀⠂⠈⠲⡬⢵⣼⣾⡿⢿⣿⣲⠄⠑⠀⠀⠀⠀⢠⣴⣿⢿⣿⣿⣿⣈⡇⠀⠀⡀⢀⠀⠀⠀⠰⠂
⠀⠀⠀⠤⡤⠀⠄⠀⠀⠀⠟⠟⢽⡏⠿⢹⣋⠅⠀⠀⠤⣀⣄⠘⠛⠛⠛⡿⠻⢿⠉⠇⠀⠠⠏⠈⢱⡀
⠀⠀⠄⠈⢷⠒⠃⡀⠀⡀⠘⠓⠘⠂⠐⠊⠡⠐⠒⠀⠘⣛⡝⠋⠑⠓⠒⠓⠐⠉⢀⠀⠒⢖⠂⠀⠦⠏⠀⠠
⠄⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠸⢿⠟⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡟⠗⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠒⣟⠛⠉⠀⡉⢹⡷⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠑⢧⣴⣶⢆⡀⡀⠈⢓⣶⣉⣻⠤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⡔⢶⠶⢤⡀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⢻⣿⣿⣷⣄⡀⠐⢾⠛⣾⡗⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠷⢻⢠⣿⠆⢿⢻⠉⠛⠚⢳⡞⢺⠹⡕⣿⠦⣄⢀⠀⠀⠈⢿⡿⡿⣻⣧⣰⣿⢸⣿⡬⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⠋⣿⡄⣸⢸⠀⢀⠀⣸⠇⠀⠀⠀⠀⢣⣸⣮⠙⠆⠀⢠⣿⣧⣿⣿⣿⣾⣿⣵⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣠⢇⣶⣉⣠⠇⣼⢀⣾⣧⣿⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠘⠛⠋⣉⢹⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⡟⠛⠉⣿⠁⠀⣽⠀⠀⢶⡋⢼⠀⠀⠀⠀⠀⠀⠀⢀⡈⣠⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣿⠀⢠⡟⠀⠀⠈⡇⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣿⠀⡼⠀⠀⠀⠀⡇⠲⢤⣄⣀⣤⠤⠶⠋⠀⠀⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣻⣿⠃⠀⠀⠀⠀⣭⣀⣤⠶⠗⠠⠤⢤⠤⠤⠼⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣀⠀⠀⠀⡿⢹⠀⠀⠀⠀⠀⡏⢀⣠⠴⠛⠀⢀⡀⠀⣠⠄⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⢲⡾⠃⣼⡄⠀⠀⠀⠼⠛⣿⠁⠀⠀⠀⠀⢳⠞⠁⠀⢲⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣇⠈⠁⠳⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⠁⠀⠀⣸⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢰⡟⠳⣄⡀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⢰⠏⢹⡿⠁⠀⠀⠀⣀⡠⠔⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠹⣤⣞⣁⣠⣚⣀⣀⣁⣀⠀⣴⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢄⣀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⢉⡀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠉⠓⠶⢤⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⠀⠀⠀⠀⠸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡐⠶⠶⢤⣤⣤⠶⠶⠶⠮⢭⣀⠀⠉⠳⣄⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⠷⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⠳⣄⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⣫⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻
⠀⠀⠀⠀⢀⡴⣫⠟⡳⣿⣶⣴⡤⠄⠒⠚⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣾
⠀⠀⠀⠀⣿⢠⡇⢸⡀⣇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠘⠷⣷⡀⠳⡽⠄⢸⣄⠀⠀⣀⣀⣤⣦⣤⣀⣀⣠⣤⣤⣤⠤⣴⣶⣶⣋⣥⣦⣤⣦⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠛⠛⠋⠉⠉⠉⠁⠀⠈⠉⠙⠻⢦⣤⡖⢚⡵⠋⡈⠋⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣴⣎⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⠿⠿⠿⡿⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⡠⠐⣲⣷⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⠭⠁
⠀⠀⠀⠀⡴⠛⣻⣟⣿⣡⢾⠏⠚⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣷⠏⣯⡉⠀⠀⣠⣶⡒⣂⣤⣤⡀
⠀⠀⠀⠀⠀⢸⠟⠹⠓⡹⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠁⡙⢀⠀⠀⠋⠘⢷⠈⠋⠗
⠀⠀⠀⠀⢀⠎⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⡀⠀⠑⠠⡀
⠀⠀⠀⡠⠃⠀⡠⠋⠀⠤⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡈⠑⠀⡀
⠀⠰⠞⢁⣴⠟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠗
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⢿⠿⡿⡿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢰⣧⣀⣀⣤⣤⠶⠞⠉⢷⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠈⣩⣭⠀⠀⠐⠛⠃⠘⣧⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣦⡀⠀⠶⠛⠃⢠⡾⠁⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷⠈⣷⠈⠛⠶⢦⡤⠾⠋⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⠛⠛⠛⠛⠛⠛⣿⠉⠀⡿⠀⢰⡆⣀⣀⣠⣤⠶⠟⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢀⡿⠀⢰⡇⠀⣾⠁⠈⠉⠁⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡻⢷⣶⠶⣂⡾⠃⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡎⠉⣾⠋⠀⠀⣸⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠻⣦⡀⠀⠟⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⣤⣤⣄⠀⢻⡆⠀⠀⠀⣿⠀⢀⣀⣀⣀⣀⣤⣤⠤⠴⠾⠗⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣤⣤⣤⡄⢸⡇⠼⠿⠿⠿⠿⠿⠀⣿⢠⣤⣾⣧⣶⣿⣭⣬⣭⣥⣤⣤⣤⣤⣤⣤⣤⣴⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⠶⠶⠶⠶⠶⠶⠾⠿⣦⠀⣿⠀⠀⢠⣤⣤⣤⡤⠻⣆⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⡛⠛⠛⠛⠛⠛⠛⠛⠋⠀⣿⠠⠤⠤⠀⠤⠤⠤⠀⠹⣆⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠇⠀⠙⠇




⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠻⠀⠀⠀⠀⠀⣀⡩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠉⠁⠟⠀⠀⠀⠘⠠⢤⣤⢤⠜⠃⠀⠀⠙⠃⠀⢠⠴⣯⠈
⠀⠀⠀⠀⠀⠈⢆⠀⡬⠁⠀⠀⠀⢰⡦⠤⠀⠀⠄⣴⠀⠀⢀⠀⠀⠀⠘⡆⠀⠀⠀⢻⡾⠿⣀⠀⠀⠀⠀⠀⠈⠂⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠀⠀⠠⠄⠀⠀⠀⠀⠘⠇⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠼⠀⠀⠀⠀⠐⠺⠉⠀⠀⠀⠀⠧⡀⣈
⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠖⠀⠀⠀⠀⠀⣓⡀⠀⠀⠀⠀⠷⠆⢀⠀⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⢩⠙⢢
⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠊⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⢏⡇
⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠶⠿⠶⠦⣴⡀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠀⠀⠈⢄⠀⠀⠀⢠⣴⠃
⠀⠀⠀⠀⠀⢀⣞⢑⡀⠀⠀⣈⣱⠀⠀⠀⠀⠀⠐⠧⠀⠀⠀⢻⠃⠀⠀⠈⠀⠄⢀⢠⠀⢸⠀⠀⠀⠀⠁⠲⡄⠊⠁
⠀⠀⠀⠀⠀⣨⡉⠲⠅⠠⠀⢨⣟⠀⠀⠆⠀⠀⠀⠐⣴⠀⡜⠀⠀⠀⠀⠈⠁⢰⡀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⢹⣇⣀⣀⡀⠀⢸⣿⠀⠄⠘⠀⠀⠀⠀⠛⠀⠃⠀⠀⠀⠀⠀⠰⠐⠤⠚⠀⠊
⠀⠀⠀⠀⠀⠀⠙⠦⠧⠤⠤⠼⠋⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠚⠀⠀⠀⠀⠀⠲⠤⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠂⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣘⣷⣤⣧⣾⡻⠋⠉⠙⠛⠲⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣣⠅⠼⠘⠞⠒⠝⠸⠞⢀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣬⣭⣻⣿⣿⠵⠾⠿⠿⠒⠶⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⢾⡿⢛⡿⣯⣛⠟⠻⣶⣤⡈⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠁⠞⣵⣿⡆⣇⠙⣦⡀⠈⠙⠆⠙⠅⠀⠀⠀⠀⣠⣼⣷⡛⣚⠷⠦⠀⢀⣳⣠⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠋⡄⣤⢻⣿⡄⠹⢶⣽⣿⣄⠀⠀⠀⠐⡀⠀⠐⣣⢞⢿⣷⣬⠈⢳⢤⣴⠞⣻⣿⠛⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢡⠻⠘⣿⡇⠘⠀⢹⡷⠙⠐⠆⠀⠀⠀⠀⣸⠧⠈⠈⣿⣟⢷⡀⢸⡏⢺⡏⢌⠓⣆⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠙⠀⠀⢠⡀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠸⣿⡁⠀⠀⠀⠁⠂⠰⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠦⣄⡀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠈⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠠⡀⠀⠈⠙⢦⣀⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠤⠬⠯⠿⠿⠤⠴⠖⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠻⣆⣤⡀⠀⠀⠹⣿⡄⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢈⣉⡀⣠⣤⠴⠚⠋⠀⠀⢠⢴⠖⠈⠀⠀⠤⠐⠂⠙⢿⣯⢦⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣤⡤⠶⠶⠶⣶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠈⠐⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⣯⣷⡀⠀⠈⠳
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⡤⠤⢤⠤⣤⡤⠂⢀⡤⠖⠲⠿⠟⠛⠋⢀⡾⠀⠀⠀⠀⠀⢀⣤⠖⠒⠈⠁⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠶⢞⣋⣩⣥⣤⡤⣶⢶⡶⠶⢶⣦⣤⣄⣀⣀⣀⣠⣤⡤⡶⠚⠋⠀⠀⣀⣀⠤⠚⢉⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠠⠤⠤⠤⠤⠴⠶⠖⠒⠒⠂⠉⠉⠉⠉⠀⣀⣀⡤⠨⠀⠀⠴⠒⠊⠁⢀⡀⠄⠚⠁⠈⠀⠀⢀⣜⠛⣋⣲⣆⣤⡤⠟⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢉⣉⠥⠀⠀⠀⠀⣀⠠⠄⠀⠲⠉⠀⠀⠀⠀⠀⣠⡖⣥⣦⡾⢸⡞⠈⢙⡓⠢⠄⠀⠀⠀⠀⠀⣸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠒⠒⠒⠒⠚⠉⠀⣠⠴⠒⠋⠉⠀⠐⠂⠀⠠⠂⠀⢀⠤⠐⠛⠱⠋⠽⠇⠀⠙⠋⠙⠛⠑⠃⠀⠀⠀⠀⠈⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⡟⣧⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⣀⡴⠞⡻⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⣿⠀⠀⠀⠀⠀⠀⣿⢸⣿⣇⠀⠀⠀⢠⡾⢋⡴⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢻⣄⠀⠀⠀⠀⠀⣿⢸⡇⣿⡀⠀⠀⣾⠀⡾⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⡀⠀⠀⠀⠀⢹⣄⠻⣄⠉⠛⢶⣤⡀⢸⡇⢸⡇⠸⣇⠀⠀⢻⡄⣷⠈⣷⠀⠀⠀⠀⠀⢀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠲⣤⡀⠀⠈⠻⢦⣈⠙⠲⣄⠈⢿⣾⠁⢸⡇⠀⢿⡄⢀⣼⠃⣿⠀⢹⡆⠀⠀⣀⡴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡑⢤⡙⠳⢤⣀⠀⠙⣦⠀⢻⣆⣸⣿⣤⣼⣧⣤⣼⣿⡟⠉⣠⠟⢀⣾⣃⣤⠞⢩⡖⣿⠋
⢀⣤⣴⣦⣄⠀⠀⠀⠀⠀⠀⠈⠳⡄⠙⢦⡀⠉⠓⢶⣿⡶⠟⠋⠉⠁⠀⠀⠀⠀⠈⠉⠙⠻⢿⣤⣾⠟⠋⣠⡴⢋⡼⠃⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⣶
⠾⠛⠳⢦⡈⣷⣄⠀⠀⠀⠀⢀⣀⣹⣆⠀⠻⣦⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡾⠋⢠⡞⠁⠀⢀⣴⠞⢛⣉⣉⣉⠙⠛⣩⡿
⠀⠀⠀⠈⢷⡹⣍⡛⠿⠿⠛⠋⠉⠙⠻⢷⣴⠟⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣴⣿⣀⣀⣴⠟⣡⠞⢩⡴⠶⠶⠶⠟⠋
⠀⠀⠀⠀⠈⠻⣦⣉⡛⠚⠛⠛⠛⠲⣦⣼⠏⠀⣠⠶⠚⠋⠻⠿⢷⣴⣿⠀⠀⣾⣆⣤⣶⣟⣿⠓⠶⣦⣄⠹⣏⠉⠉⣁⡴⠃⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⣦⣼⠇⠀⣀⠁⢠⣶⣿⣿⣿⣿⣿⣿⠂⠀⢻⣿⣿⣿⣿⢿⣿⣦⠈⠙⣆⢻⡟⠛⠉⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠖⠛⣿⠀⠀⠻⠷⠿⢿⣷⣯⣻⡼⠟⢿⠀⠀⢸⡏⠿⣿⣧⣽⣽⠿⠳⠞⠃⠈⣿⠻⠿⢧⣤⣀⣀
⢀⣀⣠⣤⣶⣒⣚⣛⣉⣀⣀⣀⣀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⢸⣷⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣈⣉⣙⣛⣿⣶⣦⣤⣤
⠈⠙⠛⠛⠻⠿⠧⣤⣤⣀⣀⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣏⠀⠀⠀⣿⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⣀⣀⣤⡤⠴⠶⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡽⠿⠛⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⠟⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡶⠚⠛⠛⣷⡀⠀⠀⠀⠀⠀⣠⣀⣀⣠⣴⣤⣤⢶⣤⣄⣤⣄⠀⠀⠀⠀⠀⢠⣿⣄⠀⠻⢤⣤⣤⣤⣄⣀
⠀⠀⠀⣀⣀⣀⣠⣼⠇⣰⠏⣠⡤⠴⣾⠟⠳⣄⠀⠀⠀⠀⠟⠛⠛⢻⣿⠿⠷⠛⢻⡟⠛⠛⠀⠀⠀⠀⣠⣿⡀⠉⠳⠶⠤⠶⠶⠶⢬⣙⠳⣄
⠀⣴⢟⡭⠥⠤⡤⠴⠞⢁⡾⠃⠀⣰⠏⠀⢀⣿⢦⣄⠀⠀⠀⠀⠀⠀⠙⠷⣶⠶⠟⠁⠀⠀⠀⠀⣠⣾⡃⠈⢿⣦⣤⣠⣤⠴⠶⠾⠶⣌⢣⣹⡆
⢸⣷⡶⠟⠛⠓⠶⠶⠟⠋⠀⠀⣰⠏⠀⣴⠟⠁⣀⡽⠷⣤⣀⡀⣂⣤⡀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣅⠈⠙⢦⡀⠹⣆⠀⠀⠀⠀⠀⠀⠙⢦⣽⣟⣳⣶
⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⠞⢁⣴⢾⡟⠀⢠⡟⠉⣙⣿⡿⠿⣶⡶⠶⢾⠟⢻⡇⢀⡟⠉⠻⣦⣀⠙⢦⡘⢧⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣼⣥⠞⠋⠀⠘⣷⠀⣾⠀⣸⠏⠈⣿⠀⢹⠀⠀⣿⡄⠈⢧⠈⢷⣄⠀⠀⠙⠳⢦⣉⢮⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠁⠀⠀⠀⠀⢸⡇⢸⡆⣿⠀⠀⢹⡆⢸⠀⢰⡟⢳⣄⠈⠳⢤⡉⢷⡄⠀⠀⠀⠈⠛⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⢀⣼⠃⡼⢀⡿⠀⠀⠘⣧⢸⠀⣾⠁⠀⠉⠛⠷⣦⠹⡄⢿⠀⠀⠀⠀⠀⠀⠈⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⡜⢁⡾⠃⠀⠀⠀⢻⣼⢰⡇⠀⠀⠀⠀⠀⢸⡆⠇⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⣯⡾⠋⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⢸⣰⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠈⢿⣗⢸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿

⠀⠀⠀⠀⣠⢤⣀⡀
⠀⠀⠀⣼⣿⣀⣀⣈⣉⣓⠒⢲⣿⡻⠭⠩⣍⣙⣓⣒⣒⣒⠲⠦⠤⠤⣀⣄⣀
⠀⠀⢸⡿⢿⣧⠀⠈⠉⠉⠉⠉⠙⣿⠀⠀⢹⡯⠭⠭⠭⢿⣿⡛⢇⠀⢰⣿⡿⠃
⠀⠀⠈⠻⣶⣿⠛⠛⠻⠿⢿⣿⣿⢿⣶⡶⣾⢿⣷⣤⣤⣤⣤⣥⣤⡄⠀⢧⡀
⠀⠀⠀⠀⣿⣻⣤⣤⣤⣤⣬⣭⣿⣀⣀⣀⣿⣶⠿⠶⠶⠶⠶⢦⣀⠀⡠⠄⠋⠷⠤⢄⡀
⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠈⠹⣿⣏⠉⢹⡿⢿⣆⣀⣀⣀⣀⣈⣉⠟⠈⠁⠄⠀⢀⣤⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠛⢻⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⣸⣿⣧⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣤⣤⣤⣤⣤⣤⡴⠦⠤⣶⣶⣶⣤⣴⢆⣿⣿⣿⣎⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⣿⣿⠋⠉⢿⣷⠀⣴⣿⡿⣿⣿⢟⣾⣿⡿⢿⣿⣮⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠘⡆⠀⢸⣿⢀⣿⠿⠇⠀⣬⣾⣿⣿⣶⣶⣿⣿⣧⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠱⣄⢸⣿⣜⡝⠀⣠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠬⠭⠭⠖⠒⠚⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠏⣿⣿⣿⣿⠿⢿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣾⣾⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀⠹⢿⣿⣿⣿⣿⠿⣟⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⢤⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠠⡈⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⢀⣄⠀⢠⣦⡀⠀⠀⠘⣆⠀⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢀⣾⠬⠑⠞⠐⠛⠳⠦⣄⣽⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡇⠠⡄⠀⠀⠆⠀⠀⠈⠋⢹⠎⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⠀⠀⢀⡞⠉⠀⠙⢒⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣈⠳⢤⣀⣉⣉⠀⠀⠙⡷⡉⠉⠓⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡞⠁⠀⡹⣅⢀⡰⣳⠁⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡆⠑⠊⠉⠀⠁⣸⠀⠀⠀⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⣧⣀⡀⠀⠀⢠⠃⠀⠀⢰⠃⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠉⢉⡟⠉⠹⢶⡀⡟⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠓⠶⠦⣤⠤⣤⣼⣧⣠⣾⣛⣼⣁⣀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠇⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠘⢇⡀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣍⣓⠦⢤⣀⠀⠀⠀⣰⠋⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⡟⠉⠛⣻⠁⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣀⣴⣁⣀⣀⡴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⠿⣿⠻⡿⠿⢿⣯⡭⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠻⠶⣿⣛⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣮⡳⡀⠀⢸⣭⣭⣭⣭⠷⠶⠋⠁
⠀⠀⠀⠀⠀⠀⣰⣟⣿⣿⣿⠿⣦⡔⠻⡟⠋⠻⡟⠉⠁
⠀⠀⠀⠀⠀⣼⢏⣾⣿⢿⠃⠀⠈⢧⡀⠳⣄⣠⠃
⠀⠀⠀⠀⢰⡟⣾⣿⣿⣿⠀⠀⠀⠀⠉⠀⠉
⠀⠀⠀⠀⣿⣇⠿⠿⠿⣻⡇
⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠃




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣷⡿⠿⣿⣿⣿⣿⠿⣻⣿⣯⣵⣾⣿⡆
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣯⣝⣻⠿⠏⠀⠀⠀⠉⠀⠈⠐⣦⠀⠹⣯⣶⠿⢟⣛⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⢲⣟⠿⠿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣤⣀⠀⠀⠀⢲⣀⣀⣀⣀⣰⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣤⡼⠿⢷⣶⣶⣿⣿⠛⢻⣟⣋⣥⣤⣤⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣾⠿⢻⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠠⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠏
⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⢛⣛⣛⣛⣛⣿⣿⡇⠀⠀⢰⢸⣿⣿⣿⣿⣿⣛⡛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⠃⠀⡀⢸⣾⣿⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣤⣶⣿⣿⣾⣿⣿⣷⣀⣀⣀⡀
⠤⠤⠤⢤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣤⡤⠤⠤

⠀⢰⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⡉⠳⣄
⠀⢰⡄⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡈⠳⡄
⠀⢸⡇⠀⠀⠀⣿⣉⣉⠁⢤⣀⣤⠀⣤⣤⡄⢨⠠⣿⡄⣭⠀⣤⣤⣄⢀⣤⢤⣤⠀⠀⠀⠀⠈⢿⣿⣿⣆⠙⢦⡀
⠀⢸⡇⠀⠀⠀⣿⠉⠉⠁⢈⣿⣅⢸⣇⢀⡀⢸⡁⣿⠀⣿⠀⣿⠀⣿⢸⣇⢀⣿⠀⠀⠀⠀⠀⢀⣽⣿⣿⠗⢀⡿
⠀⢸⡇⠀⠀⠀⠙⠛⠛⠃⠛⠀⠙⠀⠙⠛⠁⠘⠁⠙⠃⠙⠀⠋⠀⠋⠠⣝⣩⡟⠀⠀⠀⠀⣠⣿⣿⡿⢃⡴⠋
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢠⣾⣿⡿⢋⣴⠏
⠀⠘⠷⠶⠶⠶⠶⠶⠶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⡶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠤⠼⠽⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠽⠧⠄⠤⠤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⣠⠟⣠⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⣠⠞⢁⣴⣿⣿⠏⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢠⡾⢁⣴⣿⣿⠟⠁⠀⠀⠀⠀⣿⣤⣼⡃⢠⡖⢲⡄⢰⡶⠂⣶⢰⡶⠺⡆⢠⡞⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠈⢷⣄⠹⣿⣿⣷⡀⠀⠀⠀⠀⣿⣤⣼⡇⠹⣆⣰⠇⢸⡇⠀⣿⢸⡇⠀⡇⠸⣧⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠙⢷⣌⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠙⢦⡘⠛⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠙⠉⠉⢹⠻⡟⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⡀⠀⠀⣀⣀⣀⢀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠚⠀⠂⠀⠉⠱⠟⠃⠈⠉⠋⠀⠛⠀⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⣞⠉⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡔⠒⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠐⡀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠁⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣋⡄⠀⠠⠆⠀⠀⠀⠀⠀⡂⣺⠦⠋⠄⠀⠄⠀⠉⢍⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⢀⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅⣀⣑⠂⠀⠀⠀⠀⠾⠟⠻⣷⡀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣷⠲⠀⠀⠀⠀⠀⠀⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣀⠂⠐⠒⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠐⠀⠀⠙⠁⡀⡀⠄⣰⠦⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠤⠖⢇⣠⣀⡤⣧⠀⠀⠀⠀⠀⢠⣅⣀⡤⠐⠛⠲⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⠑⠊⡀⢿⠃⡀⠀⠀⠀⣿⠉⠑⠋⠉⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⣀⣀⡀⠀⠘⠋⠙⠆⢉⠒⠛⠐⠁⢀⡄⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠴⠴⡾⠹⠤⣀⣰⣠⠖⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⣀⠀⠀⠀⣠⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠤⢤⡖⠒⠖⡇⠀⢀⠀⣿⠈⠑⠒⡋⠁⠈⠉⡦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠕⠀⡠⠒⠊⠉⠀⠔⠓⡴⣉⡊⠁⠃⠀⠒⠀⠀⠀⠐⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠰⠀⠀⠔⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣴⡃
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠴⠋⠁⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠂⠒⠐⠒⠒⠂⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠐⠒⠒⠈⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣀⠀⠀⠐⠂⠀⠠⠀⠀⢒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⣠⣄⠀⠀⢀⣑
⠀⠀⠀⠀⠀⡄⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⡄⠒⠨⡀⠘⠿⢟⠀⠐⢿⡿⠀⢠⠒⠂
⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠈⠀⠀⠀⠀⠂⠀⢀⠐⠂
⠀⠀⠀⠀⢰⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡎⢢⡀⢀⡠⢊⠐⣂⠖⢤⡤⡀
⠀⠀⠀⠀⠈⠁⢸⡀⡀⠀⣀⢀⢀⠀⣀⢀⢀⣀⣀⣀⡸⣫⡄⠊⠁⠙⠀⢠⡄⠀⠀⠛
⠀⠀⠀⠀⢀⢠⢸⠉⠉⠉⠉⠉⠈⠁⠁⠉⠉⠉⠉⠙⠁⠈⠀⠘⠓⠗⠀⣀⠀⠸⠶⠆⢀
⠀⠀⠀⠀⠸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⢀⡉⠀⠶⠄⣄⡽
⠀⠀⠀⠀⢀⠸⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠧⠠⠀⠐⠁⠠⠂
⠀⠀⠀⠀⠘⢸⢸⡇
⠀⠀⠀⠀⠀⢸⣈⠓⠒⠚⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⣉⠀⠀⠀⠀⠂⠀⠂⠀⢂⠐⡇⠀⠀⠀⠀⡀⢰⡄⢀
⠀⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢐⡿⢀⠀⠀⡻⠀⠄⠀⠀⠘⠀⠉⠂⠠⠐
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⡔⠈⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢘⣽⣿⣿⣿⡿⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠐⠲⢮⣼⣿⣿⡟⣱⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣤⣄⣀⣀⢀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡂⠉⠄⠀⠻⣿⣯⠻⣿⣿⣿⣿⣿⣿⣵⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⢿⣧⡀⠘⠀⠀⠈⠀⠀⢛⠁⠈⢹⣿⣿⣿⣿⣿⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⢷⠀⠀⡀⠀⠀⠠⣼⣇⣠⣿⠛⣁⣾⡿⢿⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⡀⣠⡀⠀⠀⠀⠒⢺⣿⠿⠋⠸⢗⡳⢝⣸⠃⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣷⠀⠀⣀⢤⠈⠁⣠⣶⣫⡷⠿⣓⣷⣚⡭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⣿⡿⠋⠀⢰⢧⣿⡄⠀⠙⢋⠒⡁⢬⡭⠭⠅⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣠⢎⣿⣉⣳⡀⠀⠀⠙⢿⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣳⣿⣿⣿⣿⣷⣄⠀⠀⠀⠙⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⣿⣿⠟⠉⠁⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⣠⠞⢋⣽⣿⣿⣿⣿⣿⣖⡺⠭⠒⠃⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⢌⣁⣴⣿⣿⣿⣿⣿⣿⣿⣷⣖⣮⣭⣥⠀⠀⠀⠀⠀⠀⠠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠫⣕⠪⠿⠛⠉⠀⠉⠙⠻⠿⣿⣿⣿⣿⣧⣧⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣶⣵⠶⠚⢉⣀⣤⠴⠀⠈⠉⣽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢈⠙⠋⠐⢊⣉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⠀⠀⠀⣠⣤⣾⣵⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣶⣦⡷⢷⡏⠉⠈⠐⡀⠂⠔⠁⠀⠀⠀⠀⠀⠁⠠⢾⣿⣿⣿⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠋⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡆⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡴⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡉⠙⢿⣿⣿⣿⣿⣿⣷⡄⠀⠈⠛⠿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⢿⣿⣿⣿⣿⣿⣿⣄
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢻⣿⣿⣿⣿⣿⣿⣆
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠻⣿⣿⣿⣿⣿⣿⣧
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣇
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣄⡀
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⣸⣿⣿⣿⣿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿
⠀⠀⠀⠉⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣤⠾⠋⠉⠀⠀⠀⠀⠈⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠋⠙⠛⠲⠦⣄⡀
⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⣷⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⣦⡹⣦
⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣷⡄⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣠⣿⣧⢻⡆
⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⣸⣿⣿⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠈⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀⢻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠈⠛⠷⣤⣀⠀⠀⠀⠀⣀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢶⣤⣤⣤⣴⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠂⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠁⢀⠄⠐⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠃⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⡄⠀⠑⠀⢀⠀⠀⠐⠃⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⢠⣤⠀⢶⠀⢠⡄⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⣿⠀⠈⠁⠘
⠀⠀⠀⠀⠀⠠⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠁⠈⠉⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠄⠀⠈⠆⠀⠀⠀⠂⠀⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠒⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠐⠊⠀⠂


⠀⠀⠀⠀⠀⣐⢄⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠂⠀⠀⠀⠀⠁⠉⠁⡢⠀⠀⠀⠀⠈⠉⠀⠠⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠉⠠⢤⣀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠒⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠐⠂⠀⠀⠀⠀⠈⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⣤⣤⣤⣤⣤⣤⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠖⠉⣭⠿⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣎⣀⣼⡠⠃⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣛⠯⣭⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⢆⠀⠀⠄⠐⢄⠹⡂⢠⠈⢖⣠⠂⢠⠀⡀⣀⡀⠤⢀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠑⠦⣸⡄⢄⠻⣇⡜⢣⣸⢁⢂⣾⠟⠋⠁⣀⠔⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣧⡀⠰⠈⢻⣬⣶⣿⠞⠳⣿⣿⡏⠀⠰⢀⣼⡉⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⠛⠻⣦⣴⣯⠝⠉⠀⠀⠀⠀⠉⢋⣷⡶⣋⠥⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⣑⠶⠔⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣥⠶⠿⠒⠉⠉⠀⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠠⠐⠉⠀⠔⠚⢅⣻⣿⠀⠙⠒⠂⠀⠀⠑⠚⠋⢈⣿⢌⡵⠒⢀⣤⠄⠂⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⣠⠔⢲⡿⢋⡹⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣒⠻⢍⠑⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠖⠁⢂⣡⡞⠟⢭⣷⣤⣀⣀⣀⣠⣴⣯⠟⠉⠻⣦⡅⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⢋⠘⠂⣡⣿⣿⡟⠷⢻⡟⢯⠻⣅⡘⠀⠘⣷⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠄⠉⣀⣠⣴⢾⠏⠌⣸⡏⢶⠋⣿⣄⠣⠹⡏⢦⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠉⠁⠀⠀⠐⠀⡔⠁⢧⠀⠀⠸⣄⠑⠄⢩⠀⠌⠢⠑⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⡶⢯⠀⠀⠀⠁⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢐⠙⠃⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⢾⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠙⠶⠄


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣖⠺⣄⡙⢷⣦
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠉⠓⠿⣷⣾⣄⣀
⠀⠀⠀⠀⠀⠀⢸⣁⣀⠀⠀⠀⠀⠉⠙⠻⠿⣖⣢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⣰⠁⠉⠛⠶⢤⡀⠀⠀⠀⠀⠀⠉⠛⠶⢭⣑⠲⢤⡀
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢰⠷⠴⣦⣤⣀⠀⠀⠀⠀⠀⠈⠙⠚⠧⣴⣂⢄⣀
⠀⠀⠀⠀⠀⠀⠙⠓⠦⣤⣀⡾⠀⠀⠀⠉⠙⠳⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢽⣍⡓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⡲⠤⣀⠀⠀⠀⠀⠀⠉⠑⠢⣄⣀⡤⣀⡀⠀⠀⠀⠈⠙⠓⡦⣭⣓⡢⢤⣀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣭⡓⠦⣤⡀⠀⠀⢼⡁⠀⣽⠶⡭⣕⠲⡄⠀⠀⢠⠁⡆⢈⠉⡷⢬⣝⣲⣴⣊⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡀⢯⣀⠀⠀⠉⠛⠻⠾⣤⣠⠟⢓⡖⠦⣼⠰⠇⢸⠆⡇⡇⢰⠉⡏⠳⠦⢭⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢩⡟⠲⠦⢤⣄⣀⠀⣆⠀⠺⣄⠀⢈⡿⢲⡞⠛⡷⡷⣸⢸⡇⣇⠀⠀⣿⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣼⠁⠀⠀⠀⠀⢈⡟⠳⢦⡀⠀⢙⡶⠟⠀⠱⣄⣉⠉⣹⣮⡇⣿⠀⢠⡷⠒⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⡇⠀⠀⠀⢀⣠⣞⣀⣠⠼⡇⠀⣸⠁⠀⠀⠀⠀⠀⠉⠁⠀⠙⠳⡏⢹⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⢿⣄⠀⠀⠉⠉⠉⠉⠀⠀⣷⠀⣸⠇⢀⣤⣤⣄⠀⠀⠀⢀⣠⢶⡿⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠿⣿⣶⣤⣄⡀⠀⠀⠀⣿⣠⢧⡀⠘⠿⠤⠟⠀⠀⣠⢋⡶⠲⠶⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢽⣟⣲⠾⠃⢻⠞⠁⠀⠀⠀⠀⠀⢠⡇⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠀⠸⣤⠀⠀⠀⠀⠀⠀⢸⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡾⠀⠀⠀⠀⠀⠀⣼⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⡇⠀⠀⠀⠀⠀⠀⣿⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⠁⠀⠀⠀⠀⠀⠀⢿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡟⠀⠀⡞⣹⢷⡄⠀⢸⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⡛⠺⢧⣄⡀⠙⠷⠞⠁⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⠶⢭⣽⣓⡲⣆⢀⡾⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠛

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣀⣀⣀
⠀⡇⠤⠤⠤⠬⠭⠿⠿⠷⠞⡏⠉⠉⢉⣉⣉⣉⣉⣁⣀⣀⣈⣉⠉⠉⢦⣶⠖⠒
⠀⡷⣶⡶⠶⣶⣶⣶⣶⡶⢆⠀⠀⠀⢸⠀⠀⠒⠶⠤⡄⠀⠀⢩⠉⢆⠀⠣⣤⣄
⠀⢸⣀⣀⡗⣀⣀⣀⣀⣀⣘⡿⠿⠿⢿⠀⠀⠀⠀⠈⠁⠀⠀⢸⠀⢸⠀⠀⠀⠉⠒⠶⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢸⠀⠈⠙⠛⢲⣞⣿⣿⢞⣠⡟⠠⢂⡔⢄⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⠘⠒⠒⠒⠒⠒⠚⠛⠛⠚⠋⠀⠈⠉⠒⠢⢃⣠⣤⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠓⠢⡀⡠⠒⠒⠀⠸⣶⡶⠢⡄⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡅⠀⠀⠀⠀⣸⠃⠀⢸⢀⣠⣾⣿⣿⣿⣿⣿⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣒⠁⣀⣀⣼⠛⠛⠛⢻⣿⣿⣿⣿⣶⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠐⠈⢣⢀⡨⠀⡀⠐⠈⣀⠅⠠⢇⠀⢀⡢⢸⠀⡀⠁⢀⠃⠄⢁⡊⠀⠀⢹⣿⣯⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠙⠛⠛⠛⠛⠟⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠰⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⡃⠰⠁⢻⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠿⡀⠀⠈⣽⣿⣿⣿⡿⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣀⠀⠑⠳⠾⠿⠿⣿⣡⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⣶⣤⣤⣠⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⠀⠐⡀⠈⠻⠿⠎⢻⡿⠿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⢿⣷⡀⠁⠀⠀⠀⠀⠨⡄⠀⢠⣿⠿⠻⣿⣟⣿⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⣚⣿⣴⣿⠁⡴⣟⢿⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡶⣴⣦⣬⣦⡀⠀⠀⠀⠉⠿⠋⢁⣨⣥⣪⣥⣾⣁⠤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⠇⠀⣴⢸⡇⠀⠶⡿⢛⡯⠭⠿⠽⠶⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠟⠁⠀⣠⢧⠿⢧⠀⠀⠀⠢⣶⣱⡎⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣣⣿⣶⣾⣦⡀⠀⠀⠈⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣹⣿⣿⡿⡟⠛⠳⠄⠀⠀⠀⠈⠂⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢟⣿⣿⣿⣧⣧⣄⣤⣄⣆⠄⠀⠀⠀⠀⠀⠀⠀⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⢷⣄⠐⢉⣠⣿⣿⣿⣿⣿⣿⣟⣫⠭⢔⡒⠱⠀⠀⠀⠀⠀⢐⠧⠀⠀⠀⠀⣀⣀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⡭⣞⡿⠟⠋⠛⠻⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠠⠀⠀⠔⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣤⣔⣠⡤⠖⠂⢀⣀⡉⠉⠛⢻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠃⠶⠒⣋⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣨⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠁⠀⠀⠀⡍⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣠⣴⣪⡷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣤⣼⡴⣶⠒⠂⠃⢄⠐⢄⠂⠀⠀⠀⠀⠈⠑⠠⣴⣶⣿⣿⡿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠟⠋⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⣦⡌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⢄⡀⠀⠀⠀⢸⢻⣴⢈⠈⢻⡄⠀⠐⡇⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⠤⠤⠤⠄⣴⠇⢠⡠⠀⠹⠀⠀⠀⢸⣿⠆⠗⢃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢑⣄⠀⠀⠀⠀⠀⣀⢀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⢘⡛⠀⠀⠀⠀⠀⠀⠀⠺⣶⣺⡛⠤⡼⠀⠀⠀⠠⣿⡇⣤⣄⢀⠐⢺⠈⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯⠤⢀⣈⠈⠁⢹⠋
⠀⠀⠀⠀⠀⠀⢸⡟⡛⠋⢻⠆⠀⠈⠀⠛⣹⢿⠛⠉⠀⠀⠀⠀⠀⣿⡏⣦⠈⣤⣄⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣆⠘⢩⣄⡴⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⣠⣖⣧⣤⣀⡄⠺⡏⠀⠀⠀⠀⠀⠀⠀⣽⡉⣄⡿⠀⢀⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠁⢂⠎
⠀⠀⠀⠀⠀⠀⠀⢻⣯⡭⠤⠈⢠⡈⠉⢰⢢⠃⠀⠀⠀⠀⠀⠀⠀⣿⢷⡴⠟⠩⢾⡃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⠀⠀⠈⣧⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⡿⣤⣀⠀⠶⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠀⠀⠀⠿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⠀⠀⠀⢖⣠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠀⢀⣀⣀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡷⢀⡌⠁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠢⣠⡀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣌⣄⣴⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠒⠂⣀⠶⠶⠔⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡆⠀⠀⠀⠀⠘⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣤⠄⠉⠉⢀⠀⠉⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⢿⡄⠐⠐⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡀⢀⡀⠀⣄⠈⠇⣐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⢿⡆⠀⠀⠰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⣀⣶⠒⣳⣦⣿⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⢾⣷⣄⣤⣼⢘⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣯⣩⠋⠁⠀⢨⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢟⡉⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⢰⡧⠳⠢⠔⡀⢀⡸⠰⠆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡛⢁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⠜⠁⠀⠀⠙⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣰⣀⣄⠄⠈⢀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠁⠘⠈⠺⠋⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⠀⠀⢀⣴⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠚⠇⠀⠐⢢⡀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠒⠒⠒⠛⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠲⠒⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠉⠚⠂⠀⠀⠐⠀⠈